Junze Deng

Junze Deng, Yuan Cheng, Shaofeng Zou et al.

Contextual Markov decision processes (CMDPs) describe a class of reinforcement learning problems in which the transition kernels and reward functions can change over time with different MDPs indexed by a context variable. While CMDPs serve as an important framework to model many real-world applications with time-varying environments, they are largely unexplored from theoretical perspective. In this paper, we study CMDPs under two linear function approximation models: Model I with context-varying representations and common linear weights for all contexts; and Model II with common representations for all contexts and context-varying linear weights. For both models, we propose novel model-based algorithms and show that they enjoy guaranteed $ε$-suboptimality gap with desired polynomial sample complexity. In particular, instantiating our result for the first model to the tabular CMDP improves the existing result by removing the reachability assumption. Our result for the second model is the first-known result for such a type of function approximation models. Comparison between our results for the two models further indicates that having context-varying features leads to much better sample efficiency than having common representations for all contexts under linear CMDPs.

Junze Deng, Qinhang Wu, Peizhong Ju et al.

Rehearsal-based methods have shown superior performance in addressing catastrophic forgetting in continual learning (CL) by storing and training on a subset of past data alongside new data in current task. While such a concurrent rehearsal strategy is widely used, it remains unclear if this approach is always optimal. Inspired by human learning, where sequentially revisiting tasks helps mitigate forgetting, we explore whether sequential rehearsal can offer greater benefits for CL compared to standard concurrent rehearsal. To address this question, we conduct a theoretical analysis of rehearsal-based CL in overparameterized linear models, comparing two strategies: 1) Concurrent Rehearsal, where past and new data are trained together, and 2) Sequential Rehearsal, where new data is trained first, followed by revisiting past data sequentially. By explicitly characterizing forgetting and generalization error, we show that sequential rehearsal performs better when tasks are less similar. These insights further motivate a novel Hybrid Rehearsal method, which trains similar tasks concurrently and revisits dissimilar tasks sequentially. We characterize its forgetting and generalization performance, and our experiments with deep neural networks further confirm that the hybrid approach outperforms standard concurrent rehearsal. This work provides the first comprehensive theoretical analysis of rehearsal-based CL.