Finite-time Convergence Analysis of Actor-Critic with Evolving Reward
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| Format: | Preprint |
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2025
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| _version_ | 1866909844620967936 |
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| author | Hu, Rui Chen, Yu Huang, Longbo |
| author_facet | Hu, Rui Chen, Yu Huang, Longbo |
| contents | Many popular practical reinforcement learning (RL) algorithms employ evolving reward functions-through techniques such as reward shaping, entropy regularization, or curriculum learning-yet their theoretical foundations remain underdeveloped. This paper provides the first finite-time convergence analysis of a single-timescale actor-critic algorithm in the presence of an evolving reward function under Markovian sampling. We consider a setting where the reward parameters may change at each time step, affecting both policy optimization and value estimation. Under standard assumptions, we derive non-asymptotic bounds for both actor and critic errors. Our result shows that an $O(1/\sqrt{T})$ convergence rate is achievable, matching the best-known rate for static rewards, provided the reward parameters evolve slowly enough. This rate is preserved when the reward is updated via a gradient-based rule with bounded gradient and on the same timescale as the actor and critic, offering a theoretical foundation for many popular RL techniques. As a secondary contribution, we introduce a novel analysis of distribution mismatch under Markovian sampling, improving the best-known rate by a factor of $\log^2T$ in the static-reward case. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_12334 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Finite-time Convergence Analysis of Actor-Critic with Evolving Reward Hu, Rui Chen, Yu Huang, Longbo Machine Learning Artificial Intelligence Many popular practical reinforcement learning (RL) algorithms employ evolving reward functions-through techniques such as reward shaping, entropy regularization, or curriculum learning-yet their theoretical foundations remain underdeveloped. This paper provides the first finite-time convergence analysis of a single-timescale actor-critic algorithm in the presence of an evolving reward function under Markovian sampling. We consider a setting where the reward parameters may change at each time step, affecting both policy optimization and value estimation. Under standard assumptions, we derive non-asymptotic bounds for both actor and critic errors. Our result shows that an $O(1/\sqrt{T})$ convergence rate is achievable, matching the best-known rate for static rewards, provided the reward parameters evolve slowly enough. This rate is preserved when the reward is updated via a gradient-based rule with bounded gradient and on the same timescale as the actor and critic, offering a theoretical foundation for many popular RL techniques. As a secondary contribution, we introduce a novel analysis of distribution mismatch under Markovian sampling, improving the best-known rate by a factor of $\log^2T$ in the static-reward case. |
| title | Finite-time Convergence Analysis of Actor-Critic with Evolving Reward |
| topic | Machine Learning Artificial Intelligence |
| url | https://arxiv.org/abs/2510.12334 |