RCCDA: Adaptive Model Updates in the Presence of Concept Drift under a Constrained Resource Budget

We thank the reviewer for the insightful comments and constructive feedback. We address the specific weakness and questions below and hope that our clarifications and planned revisions will resolve the concerns raised.

Time as the only resource

Our theoretical framework is designed to be general and is not limited to "time" as a resource. In the evaluated scenario, a model update is a discrete event represented by a general time-varying function, $\lambda(t)$. This function is an abstraction that can represent various types of resources, including peak memory consumption or computation cost. Similarly, the resource constraint $\bar \lambda$ is an average cost constraint over this general function $\lambda(t)$. For our experiments, we chose $\lambda(t)$ to be a constant-update computation cost, which makes the resource constraint equivalent to limiting the frequency of updates, effectively framing time as the only resource. We did this as it allows us to compare performance differences between policies as a result of their update timing decisions. Furthermore, such setup avoids the complexities of precisely simulating hardware-dependent metrics, which can vary significantly based on the underlying system. As such, Figure 2 uses "Time step" as the x-axis because it represents the discrete decision to spend resources at a given time in our problem formulation, making it a fair comparison between the evaluated policies.

Computation and memory overheads of RCCDA

The main computational and memory bottlenecks in RCCDA are associated with the gradient estimation function $\hat g(\cdot)$ and the history buffers $\mathcal H$. The choice of the estimation function is left to the agent, allowing for flexibility given memory and time constraints. In our experimental section, we utilized gradient estimation function $\hat{g}(\cdots) = K_{d} (f_t-f_{t-1})$, as per line 315 in the manuscript. This estimation function only requires storing the previous loss value, resulting in minimal increase in memory overhead. All other parts of our proposed algorithm are either computed as part of the operation of the system, such as $f_t$ (independent of the decision process), or take minimal computation time. Additionally, the virtual queue keeps track of a single scalar value and only requires a single update at any time $t$, keeping the added memory and computational overhead to a minimum. Overall, compared to the introduced baselines, our algorithm performs a few more constant-time operations on average, but these add negligible computational and memory cost.

Regarding the inference time, in our framework, we model the agent as being deployed in the evaluated environment. As such, the agent runs the evaluation task at every time $t$, modeling continuous operation, and making the inference time independent of the decision process. Similarly, when it comes to the training time, that time is captured implicitly in the abstract model update cost $\lambda(t)$.

Continual data monitoring

Thank you for pointing out this opportunity to improve the presentation. To clarify, what distinguishes RCCDA from the existing baselines is the cost associated with the monitoring operation. Traditional TDG or drift detection methods often require monitoring the data distribution properties, or sequentially evaluating all datapoints. In contrast, RCCDA monitors only the model's inference loss. The loss is a lightweight, scalar value that can be computed by the evaluation process of the model's primary task. Its computation is parallelizable and is optimized through a variety of techniques. Reliance on loss makes our approach lightweight, and as discussed before, results in minimal added temporal overhead.

To illustrate this point, during the rebuttal, we conducted additional experiment that compares the operation time of RCCDA with two established drift detection methods: ADWIN, which monitors the model error rate, and Kolmogorov–Smirnov (K-S) test, which monitors the incoming data stream. We measured the clock-time taken by each method to finish detecting drift/making a decision after the initial model evaluation. We utilized the PACS dataset and a single Nvidia H100 GPU, and averaged the results over 4 different domains and 3 different seeds. The results are:

Clearly, the temporal overhead added by our method is orders of magnitude smaller compared to the established drift detection methods.

Older data distributions reemerging

Accounting for reemergence of older data distributions is an important consideration in Continual Learning, where the goal is long-term knowledge retention. RCCDA, by contrast, is designed for scenarios where adapting to the most recent data distribution is the primary objective. The goal of our work is immediate resource-efficient adaptation to a drifting distribution of a single task. This is an altogether different problem formulation from continual learning, with a different set of objective, and results in natural a trade-offs between the model's in-time performance and generalizability.

Results statistical significance

The high standard deviations of the results stem from averaging the result across different starting domains, which have highly varying performances. To illustrate this point, we can further break down the average validation accuracy and its standard deviation for all policies across the different starting domains. The result shown below is for the burst drift schedule on the PACS dataset for the update rate of $0.1$ (and using 10 seeds instead of 3):

When deconstructed in this way, our policy consistently outperforms the baseline methods, demonstrating that the high standard deviation stems from averaging over the different starting domains. This result is also true for other drift schedules and datasets, which we will include in the final version of the manuscript.

Response to questions

a. Lightweight claim: As demonstrated in our earlier response, the added computation overheads of RCCDA are minimal, supporting the claim of our policy being lightweight.

b & c. Behavior with no drift: Under no drift, the loss $f_t$ remains stable, with in the term $(f_t - \min_i f_i)$ approaching zero. As such, the likelihood of an update becomes small, diminishing the value of $Q(t)$ over time, leading to a stop in model updates, thus conserving resources. This is a key feature of RCCDA: the algorithm improves over standard gradient descent methods by not diminishing resources on unnecessary updates in low-drift environments.

d. Practical scenarios for drift: Drifts are common in single user scenarios like adapting to a user's changing interests in recommender systems, mobile devices adapting to a changing environments (lighting, seasons, weather, etc.), or real-time systems like ad prediction.

e. Realism of bounded KL-divergence: This is a standard theoretical assumption in the analysis of concept drift. It formalizes the notion that the data distribution will not change arbitrarily quickly between two consecutive time steps in practice.

f. Clarification of line 144: As seen in the new results above, drift detection operations that require data monitoring like the K-S test take significantly longer than RCCDA. On the other hand, ADWIN, by sequentially comparing model outputs with targets for drift detection, is order of magnitudes slower than the proposed RCCDA algorithm. By "resource" in this context we mean the number of operations required to determine whether a drift happened or to make a policy decision.

g. Different datasets in Eq 6: Equation 6 represents the objective of minimizing the time-averaged loss increase, which is then used in Lyapunov optimization to derive our update policy. Line 631 in the manuscript clarifies that the model difference arises from unrolling the telescoped loss $\mathbb E[f(\theta_0, \mathcal D_0)] - \mathbb E[f(\theta_T, \mathcal D_T)]$. The result is then combined with the drift-induced loss to define the Lyapunov optimization objective. The loss terms themselves come from the derived convergence bound, and the Lyapunov optimization goal is to find an approximate solution minimizing it.

h. Storage overhead of Eq 6: Equation 6 is part of the problem formulation but not the algorithm. The final practical implementation (Algorithm 1 block) does not require storing past and current full datasets. At any time $t$, the agent only needs to store the current dataset $\mathcal D_t$ reflecting the current data distribution.

i. Memory overhead of storing past gradients: As mentioned earlier, the memory overhead associated with storing the historical data of the gradients, loss values, and policy decisions depends on the gradient estimator function. In the practical algorithm implementation for our experiments, that overhead was minimal and reduced to storing just one additional scalar. The history buffers are meant to allow the agent to decide on how accurately they want to estimate the gradient magnitude versus how much computation and time they want to devote to that improving estimation accuracy.

We will address the minor comments in the final version as well.

Once again, thank you for your detailed comments! We will add all of these responses to the final version. Please let us know if there are any other questions we can answer.

Thank you for your final comments and engaging with our work. We agree that the challenge of recurring drifts is an important consideration for adaptive systems. As we mentioned before, the key problem is the trade-off between rapid adaptation to the current data distribution and retaining knowledge of past distribution in a model with finite capacity. Our proposed scheme was designed with the primary focus of immediate improvement in the current domain at the cost of generalization to previously seen domains. Although the focus of this work is not in evaluating the generalization capabilities of the models deployed in changing environments, in scenarios with recurring drifts it might be beneficial to preserve the knowledge of past distributions.

To that end, we show in the following that RCCDA can be extended with a replay buffer that retains a small fraction of data from previously seen distributions. When our policy triggers a model update, the training batch can be composed of a majority of new data and a minority of this buffered data. This mechanism helps the model retain information about past concepts, mitigating the effects of catastrophic forgetting.

To demonstrate this, we conducted an experiment comparing two scenarios under a new drift schedule where domains reappear over time. We used the same policy and burst schedules (that went over the photo, art painting, cartoon, and sketch domains in order switching every 100 steps, with the exception of the starting domain being cartoon in the first 50 steps), and modified the data compositions to simulate the following settings:

• No Buffer: The training dataset shifts entirely to the new domain at predefined intervals.
• With Buffer: At each shift, the dataset is composed of approximately $80\%$ new data, with the remaining $20\%$ being a balanced split of data from previously seen domains.

The following table presents the model's accuracy on each domain at key time steps, showing the performance just before the next drift occurs.

These results demonstrate several interesting insights. As expected, when seeing the domains for the first time, the original framework is better. However, when a domain occurs again, the buffered approach performs better or comparatively well, as long as the new domain is not too distinct compared to the previously seen ones. In general, we have a trade-off between the immediate model performance in the current domain and model generalization across all the domails. Depending on the application scenario, one can choose either the buffered or non-buffered approach, and our algorithm supports both.

Note that these results are only preliminary. A more detailed investigation into the aforementioned trade-off and use cases of a buffer-based approach would be a fascinating future work direction.

We thank the reviewer for their thorough and positive assessment. We are grateful that they found our paper's theoretical foundation robust, the results significant, and the contributions novel. Below we address the raised concern and answer the posed questions.

Loss availability

Our assumption is a standard one used in supervised drift detection methods. Establish methods like ADWIN and DDM, which operate on the error rate, also require ground truth labels in practice. We can here point to scenarios where the labeled data for loss calculation becomes available right away or with a slight delay, e.g., in tasks such as text prediction (predicted and ground truth text are both available in real time), content moderation (labels are provided through feedback), and online behavior tracking (real-time user responses).

The alternative is unsupervised drift detection, which monitors feature distributions and therefore does not require labels. However, these methods are computationally intensive. To see this, we have conducted a new set of experiments comparing the added computational cost of RCCDA with the cost of running (supervised) drift detection using ADWIN, as well as detecting drift using the (unsupervised) Kolmogorov–Smirnov (K-S) test, which analyzes the incoming data stream to detect drift. The experiments were conducted on the PACS dataset with a size of 1024 samples using a single Nvidia H100 GPU. We measured the wall clock-time taken by each method to finish detecting drift/making a decision after the initial model evaluation. The results, averaged over 4 starting domains and 3 seeds each are as follows:

The decision time of approximately two minutes for the K-S test would be prohibitive for real-time monitoring applications, making such methods impractical for the evaluated setting. Additionally, these results demonstrate that given the same assumptions, by using just the loss value for the policy decision, we can achieve significant speedup compared to detecting the drift using error rate calculation, which is the method utilized by ADWIN. We will include these results and this discussion in the final version of the paper.

Response to questions

How does RCCDA handle inaccurate/noisy gradient estimation: Our policy is designed around the Lyapunov optimization framework's virtual queue, which acts as a long-term controller. This ensures that regardless of the noise in the gradient estimation term, the long-term time-average resource constraint will be satisfied, as established by our stability analysis in Theorem 5.3. However, noisy estimates might lead to suboptimal retraining decisions at certain time steps; depending on how noisy the estimate is, the inference performance of the agent's model might deteriorate over time. Note that in our experiments, we utilize an estimation function of $\hat{g}(\cdots) = K_{d} (f_t-f_{t-1})$, which is a simple and lightweight approach to estimating the gradient magnitude with which we are able to achieve robust performance across the variety of tested datasets and drift schedules.

Can RCCDA be extended to multi-modal drift: As we utilize only loss and gradient magnitude in decision making, the theoretical analysis is generalizable to a multi-modal setting, supporting different modalities separately as well as potentially multi-modal tasks. Due to computational constraints, we only considered single-modal concept drift in the paper. When it comes to the evaluated environments, simulating the concept drift through domain changes gives us a convenient mechanism for evaluating non-stationary environments. This is also encapsulated in the theoretical analysis by the drift-induced loss term $\Delta f_{\delta}(t)$ in Theorem 5.1 and then the drift bound $\delta(t)$ in Corollary 5.2.

Computational overhead of maintaining the virtual queue: Maintaining the virtual queue adds negligible overhead. The queue itself keeps track of only a single floating point number. The update at each step involves one addition, one subtraction, and one $\max$ operation, resulting in $\mathcal O(1)$ time complexity in both time and memory, making the added overhead minimal from a resource perspective.

Benchmarks against SOTA adaptive policies: In the earlier response we have included a new comparison of times required to execute operations required to make a policy decision. In our main paper, we further included comparisons with baseline policies that guarantee adherence to strict resource constraints but are not designed with a learning objective in mind. Other retraining policies do not explicitly guarantee they will provide the desired long-term time-averaged resource utilization, and often don't even consider operating under limited resource budget [10, 11, 12, 22, 27, 28]. As such, to the best of our knowledge, the evaluated baselines, as well as the added computational complexity comparison, are a reasonable set of benchmarks to compare against. Through our experimental section we demonstrate that our policy is capable of outperforming these benchmarks in terms of recovery time from drifts under a fixed resource budget.

Societal impact discussion

This is an excellent point. RCCDA has a variety of broader positive impacts. The reduced computational load on devices coupled with maintaining overall high performance results in reduced computational load of devices, which then reduces energy consumption and lowers operational costs for individuals or organizations running models on the edge. Furthermore, RCCDA's lightweight nature makes it feasible to run on low-cost low-power hardware, allowing advanced AI capabilities to be deployed in a wider range of settings. Furthermore, by enabling on-device models to adapt to concept drifts, RCCDA allows for better personalization over time while preserving computational resources.

At the same time, we acknowledge that there might be some negative impacts associated with RCCDA as well. For example, if the incoming data streams become biased, our policy might update the model to fit the new biased data, potentially reinforcing negative sentiments. In-line with this, we did not consider adversarial settings where some malicious entity might inject the agent's data stream with malicious data, causing our policy to decide to update the model, degrading its performance. We will add the above discussion to the final version of the paper.

Once again, we would like to thank you for your time and effort invested in reviewing our paper. If you have any further additional questions or concerns please let us know, we will gladly address them.

We thank the reviewer for their insightful feedback. We appreciate that the reviewer recognized the value of providing theoretical guarantees for learning under concept drift. Below we further address the raised concerns and questions.

Assumptions in the paper.

We would like to clarify a few points on "prior knowledge" with respect to our assumptions. The L-smoothness, bounded variance, and bounded loss assumptions are standard assumptions common in most theoretical analyses of stochastic optimization algorithms. Furthermore, the assumption about bounded KL-divergence between two time steps reflects the fact that the data distribution will not change arbitrarily quickly in practice. We note that even though we make this assumption, we only utilize it to provide convergence and time-average constraint violation bounds; RCCDA does not use any prior knowledge of concept drift throughout its operation.

When it comes to the assumption of the estimate of the loss, our method uses the model's inference loss, calculated when ground truth labels are available. This is a foundational assumption for many of the most-cited methods in the concept drift literature. For instance, the widely used drift detectors we mentioned in the related works section, like ADWIN and EDDM operate by monitoring the model's error rate, which explicitly requires access to ground truth labels. While we do not explicitly try to detect or categorize the drift in our paper, assuming loss availability aligns with the standard requirements for supervised drift adaptation. Additionally, this assumption corresponds to a practical setup for many real-world systems like text or ad-click prediction, trend-tracking, or content moderation in which real-time feedback is available.

Duplicate citation ([10] and [26])

We are grateful to the reviewer for pointing out this issue. The mentioned references are indeed the same work, and we will correct this citation error of the final version.

Assumption on access to an unbiased estimate of the loss for small datasets

This assumption stems directly from being able to access the model's inference loss at any time $t$, and as mentioned beforehand, it is a standard assumption in supervised drift adaptation literature. Regarding its feasibility, consider that for a larger dataset, small parts of it may be labeled, resulting in a good estimate of the inference loss. If $\mathcal D_t$ is small, the empirical loss can result in a high-variance estimate of the true loss. However, even though the variance might increase, even for small datasets, as long as it is possible to sample a batch $\xi_t$ representative of the distribution at time $t$, the empirical loss should not include any bias for that dataset.

To address the issue with variance in the estimate of the loss, we conducted an additional experiment evaluating how adding error to the loss estimate affects the agent model's performance. The experiment was conducted on the PACS dataset, using the "burst" drift schedule. In the experiment, once the evaluation loss was calculated, a scaled value sampled from a normal distribution with mean 0, and varying degrees of variance was added to the original loss value. Mathematically, the uncertain loss is modeled as $f_t^{\text{estimate}} = f_t + \mathcal N(0, (k_u \cdot f_t)^2)$, where $k_u$ is the degree of uncertainty. The results of this experiment are available in the table below:

Naturally, with growing estimation uncertainty, we observe some performance degradation at the same update rates. Nonetheless, overall, RCCDA demonstrates a high degree of robustness to loss estimation error. The largest performance drop in validation accuracy is only about 2.5% relative to the case when the exact value of the loss is known, achieved when the loss uncertainty becomes fairly high, with an error variance equal to 30% of the loss at any given time $t$. We also observe an increase in the standard deviation of the average validation accuracy as the uncertainty grows, reflecting higher variability in model performance due to the added estimation noise. Despite that, the new result demonstrates that the proposed algorithm performs robustly even when the loss estimate is noisy. This is particularly relevant for small-dataset regimes, where inherent sampling variance would have a similar effect on the estimate of the loss.

We will add this experiment and associated discussion to the revised manuscript.

Response to questions

Why are the bounds stated for $\theta_t, D_{t+1}$ while the objective in equation (5) is defined for $\theta_t, D_t$: This is a direct result of the proof technique used for online optimization, available in appendix A. The objective is to minimize the cumulative loss over time under some resource constraint. To analyze this, we derive convergence bounds by examining the system's evolution from one discrete time step $t$ to the next. The final convergence bound arises from conducting that analysis and utilizing various techniques to provide a bound on the gradients. The Lyapunov optimization objective comes from attempting to minimize the derived convergence bound.

Single-task setting bounds relationship: Standard generalization bounds, typically on the order of $\mathcal O(1/\sqrt{n})$, measure how well a model trained on $n$ samples from a static distribution will perform on new data from that same distribution. In contrast, our work provides a convergence bound on the expected squared magnitude of the gradient for a dynamic setting with concept drift. This bound addresses a fundamentally different challenge of characterizing the model's performance over a time horizon $T$ as the underlying data distribution $p_t$ evolves. Because we consider non-stationary setting, where the distribution of the data changes over time, deriving a traditional generalization bound is highly challenging, as the standard assumption of a fixed data distribution becomes inapplicable to the considered scenario.

Relationship to existing state-of-the-art bounds: As stated in the paper, to the best of our knowledge, no prior work provides convergence and stability guarantees for model adaptation under concept drift subject to a strict, time-averaged resource constraint. Existing works on concept drift primarily focus on either detecting drift or adapting to it assuming unconstrained updates. The bounds provided in these works do not account for a restrictive resource budget that may prevent the model from updating at the theoretically optimal moments.

Thank you for your insights and effort in reviewing our paper! We will add all of these clarifications to the manuscript. If there are other questions we could answer or issues we could address, please let us know.

The authors have addressed all of my questions and comments. In addition, the paper provides theoretical guarantees in settings with concept drift, which are particularly challenging. Therefore, I have decided to raise my score to a weak accept.

We thank the reviewer for valuable feedback and for recognizing the novelty of applying Lyapunov optimization. We believe that our clarifications and new experimental results below address each of the raised concerns.

Computational cost of drift detection

We agree that our paper's core motivation would be strengthened by providing quantitative evidence demonstrating that our derived policy has much lower computational overhead than the existing methods. To address this, during the rebuttal period, we have conducted a new set of experiments comparing the added computational cost of RCCDA with established drift detection methods - ADWIN and Kolmogorov–Smirnov (K-S) Test. To detect drift, ADWIN uses sequential data processing and error rate calculation, while K-S test analyzes the statistical properties of incoming data streams. We conducted the new experiment on the PACS dataset with a size of 1024 samples and utilized a single Nvidia H100 GPU. We measured the clock-time taken by each method to finish detecting drift/making a decision after the initial model evaluation. The loss, as well as the ground truth labels and the predicted outputs required by ADWIN, were available to each method at the start of their operation. The results, averaged over 4 domains and 3 seeds each, are as follows:

These results provide concrete evidence that the overhead of existing methods may be prohibitive in many practical scenarios. For distribution-based methods like the K-S test, an overhead of approximately 126 seconds on average per monitoring step would be unacceptable for any application requiring real-time monitoring. On the other hand, for the error-based methods represented by ADWIN, the ~2480 slowdown compared to our method represents an unnecessary computational burden added on top of the computation associated with model operation and retraining under strict resource constraints. If compounded over long operation time, it could lead to much faster resource depletion than RCCDA. Additionally, while on the evaluated hardware, a 1.68ms average time is not significant, our work is motivated by resource-constrained scenarios, including on-device ML (e.g. vehicle camera monitoring with limited battery, on-device text prediction, etc) where the computational increase might be exemplified by slower hardware, resulting in the computation time required by ADWIN becoming a challenge. Furthermore, in high-performance real-time scenarios, where every millisecond of compute time is critical and can have severe effects on the operation time and performance of such devices, a lightweight, near-zero overhead policy like RCCDA is a major improvement over the comparable baselines. We will include these results along with the above discussion in the final manuscript of the paper.

How are hyperparameters determined

The parameter $\lambda(t)$ represents the time-varying resource cost of performing a model update. This parameter is system-defined, reflecting the real-world cost of an update in a given application, such as energy consumption, wall clock-time, financial cost of a GPU instance, etc. In our experiments, for evaluation simplicity, we set it to a constant value and divide it by $\bar \lambda$, the desired time-average cost. As a result, $\frac{\bar \lambda}{\lambda}$ effectively becomes the desired time-average update frequency of the agent's model. In the main experiment, we consider $\frac{\bar \lambda}{\lambda}= 0.1$, simulating a realistic resource-constrained setting, where the model can only be updated once every 10 evaluation steps. Furthermore, in the supplemental material section, we evaluate different desired update frequencies on a single drift schedule to formalize the effect of policy given different degrees of resource availability. Other tunable hyperparameters related to the decision process and the network updates were determined experimentally via grid search.

All utilized hyperparameter values are available in the "Supplemental Material: Detailed Experimental Setup, Documentation" section 1.3 and 1.4. These sections demonstrate that the proposed policy can be tuned to generalize across a variety of datasets and dynamic environments. Additionally, we included the code used to conduct our experiments in the supplemental materials, including the different settings testing a variety of hyperparameter values, which improves the reproducibility of the proposed algorithm and our experimental results.

Validation of paper's core motivation

We thank the reviewer for this important comment. The additional experiment comparing RCCDA with the existing methods demonstrates the lightweight nature of the proposed algorithm. On the other hand, the effectiveness of our proposed policy is supported by the results in Table 1 and Figure 2, demonstrating that compared to similar policies that have to adhere to resource constraints, our policy achieves robust performance, outperforming the existing baselines on a variety of drift schedules and across the tested datasets. Finally, Figure 2 demonstrates that the update rate of our frequency always tends to the desired set update frequency, validating Theorem's 5.3 claim, and demonstrating adherence to resource constraints. Thorough these experimental results and our theoretical analysis, we validate the core paper's motivation stated in our research question: "Can we develop a lightweight, resource-aware policy for dynamic model updates that (i) effectively mitigates performance loss incurred by concept drift in real-time applications while (ii) theoretically guaranteeing adherence to strict resource constraints?" In the final version of the manuscript, we will include the new experiment comparing the computational overhead with the established drift-detection algorithms as well.

Once again, thank you for your effort in reviewing our paper and providing important comments. If there are additional questions we could answer or issues we could answer we would be grateful for an opportunity for further discussion.

We thank the reviewer for the constructive feedback and the opportunity to clarify our experimental design and further validate the generalizability of our approach. We address the points regarding model diversity and evaluation modalities below.

Different capacity models

We acknowledge the reviewer's point about the importance of evaluating our method on models with different capacities. We would like to clarify that we had incorporated this in our experiments by using three distinct neural network architectures across the three vision datasets, each with varying complexity:

• For the PACS dataset, we used a custom deep convolutional neural network with residual connections to handle the significant domain shift between different image styles. The model had 11,177,223 parameters in total, all trainable.
• For the DigitsDG dataset, we utilized a more standard, shallower convolutional neural network suitable for the simpler task of digit recognition. The model had 1,907,146 parameters in total, all trainable.
• For the OfficeHome dataset, we adapted a pretrained ResNet-18 model to handle the higher complexity of more classes and larger images. During both pretraining and evaluation, we froze the initial layers and exclusively fine-tuned the final convolutional block (layer4) and our custom classification head. The model had 11,324,545 parameters in total, of which 8,541,761 were trainable.

Testing across different model sizes and architectures allowed us to confirm that RCCDA's performance is robust across varying model capacities. This aligns with our theoretical analysis, which is model-agnostic as long as the loss function satisfies the stated standard assumptions. The complete architectural specifications for each model, along with all training and evaluation hyperparameters, are provided in the "Supplemental Material: Detailed Experimental Setup, Documentation" for full transparency and reproducibility.

Different modalities

Our theoretical analysis is domain-agnostic, i.e., the provided bounds are applicable to all domains. We utilized the vision domain in our experiments as it allowed us to model the desired environment in a straightforward way and demonstrate the efficacy of RCCDA. The domain generalization datasets readily emulate concept drift, as pictures in different domains will have different underlying distributions. Furthermore, the vision models pre-trained on only a single domain performed poorly on new domains, which demonstrated the need for model updates, and allowed us to test our proposed algorithm in settings it would likely be deployed.

When it comes to utilizing other modalities, the experimental setup becomes more challenging, and simulating concept drift becomes less straightforward. To demonstrate this, we added an experiment on the MEMD-ABSA dataset [R1] - a multidomain dataset developed for textual Aspect-Based Sentiment Analysis (ABSA) task. The dataset contains reviews partitioned into five distinct domains: books, clothing, hotel, laptop, and restaurant. Similar to our main experiments, we first pre-trained a neural network - the TinyBERT [R2] model - on each domain independently. Then, each pre-trained model was deployed in an environment simulating the 'burst' drift schedule, where the domain of the incoming text data changes abruptly at specific intervals, simulating sudden shifts in the underlying distributions. However, the difference in the domains was not substantial enough to be able to simulate a meaningful concept drift well. We illustrate this in the table below, demonstrating the testing accuracy of a model pre-trained on one domain when evaluated on all other domains:

As demonstrated by these results, while the model performance drops when evaluated on unseen domains, the pre-trained model still remains fairly competitive achieving relatively high classification accuracy. This is in contrast to the vision-based tasks where different domains caused a substantial performance drop, as can be seen in Figure 2 in the main paper, where the validation accuracy drops from around 90% to around 35% the moment a new domain is introduced to the dataset. In other words, for certain tasks, the drift associated with domain changes is small. As a result, when we evaluated RCCDA and the baselines in the ABSA setting, the performance improvement was less significant compared to other datasets. The table summarizing the results for the "burst" drift schedule is available below, with an effective update rate $\frac{\bar \lambda}{\lambda}=0.01$.

Of note here is the fact that some of the baselines achieved the accuracy of approximately 80% with almost no updates - having effective average update rate of 0.001. This demonstrates that due to the small magnitude of the drift, the performance boost achieved by our method is not as significant as the performance gain achieved by model's generalization ability.

Additional dataset

To further validate our proposed solution, we conducted an additional experiment on the DomainNet dataset. Due to time constraints during the rebuttal period, we restricted the experiments to only 4 domains of the DomainNet dataset: real, clipart, painting, and sketch. We pre-trained a modified version of the ResNet-50 model on each of these domains, and deployed the pre-trained model in an environment experiencing concept drift simulated by the "burst" drift schedule, abruptly injecting new domain data at specific intervals. The effective update rate $\frac{\bar \lambda}{\lambda}$ was set to $0.1$, just as in the main paper experimental setup. After tuning the hyperparameters and evaluating the performance of the baselines, we arrived at the results summarized in the table below:

Compared to the other policies, when averaged over all seeds and domains, our policy once again achieved highest average validation accuracy, further corroborating the findings from PACS, DigitsDG, and OfficeHome from the main paper.

We sincerely thank the reviewer for their careful and thorough review of our work. We will gladly address any additional questions or concerns.

References:

[R1] Cai, Hongjie, et al. "Memd-absa: A multi-element multi-domain dataset for aspect-based sentiment analysis." Language Resources and Evaluation (2025): 1-29.

[R2] Jiao, Xiaoqi, et al. "Tinybert: Distilling bert for natural language understanding." arXiv preprint arXiv:1909.10351 (2019).