Transformers have demonstrated exceptional performance across a wide range of domains. While their ability to perform reinforcement learning in-context has been established both theoretically and empirically, their behavior in nonstationary environments remains less understood. In this study, we address this gap by showing that transformers can achieve nearly optimal dynamic regret bounds in non-stationary settings. We prove that transformers are capable of approximating strategies used to handle non-stationary environments and can learn the approximator in the in-context learning setup. Our experiments further show that transformers can match or even outperform existing expert algorithms in such environments.

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Transformers have emerged as a powerful class of sequence models with remarkable expressive capabilities. Originally popularized in the context of natural language processing, they leverage self-attention mechanisms to in-context learn new tasks without any parameter updates (Vaswani, 2017; Liu et al., 2021; Dosovitskiy, 2020; Yun et al., 2019; Dong et al., 2018). In other words, a large transformer model can be given a prompt consisting of example input-output pairs for an unseen task and subsequently produce correct outputs for new queries of that task, purely by processing the sequence of examples and queries (Lee et al., 2022; Laskin et al., 2022; Yang et al., 2023; Lin et al., 2024). This ability to dynamically adapt via context rather than gradient-based fine-tuning has spurred extensive interest in understanding the theoretical expressivity of transformers and how they might learn algorithms internally during training. Recent theoretical work has begun to analyze the various aspects of transformers.

These algorithms combine the ideas of finite-horizon approximation [Chen et al., 2022a], special Bernstein-style bonuses of the MVP algorithm [Zhang et al., 2020], adaptive confidence widening [Wei and Luo, 2021], as

We study the problem of Non-Stationary Reinforcement Learning (NS-RL) without prior knowledge about the system's non-stationarity. A state-of-the-art, black-box algorithm, known as MASTER, is considered, with a focus on identifying the conditions under which it can achieve its stated goals. Specifically, we prove that MASTER's non-stationarity detection mechanism is not triggered for practical choices of horizon, leading to performance akin to a random restarting algorithm. Moreover, we show that the regret bound for MASTER, while being order optimal, stays above the worst-case linear regret until unreasonably large values of the horizon. To validate these observations, MASTER is tested for the special case of piecewise stationary multi-armed bandits, along with methods that employ random restarting, and others that use quickest change detection to restart. A simple, order optimal random restarting algorithm, that has prior knowledge of the non-stationarity is proposed as a baseline. The behavior of the MASTER algorithm is validated in simulations, and it is shown that methods employing quickest change detection are more robust and consistently outperform MASTER and other random restarting approaches.

We investigate the non-stationary stochastic linear bandit problem where the reward distribution evolves each round. Existing algorithms characterize the non-stationarity by the total variation budget $B_K$, which is the summation of the change of the consecutive feature vectors of the linear bandits over $K$ rounds. However, such a quantity only measures the non-stationarity with respect to the expectation of the reward distribution, which makes existing algorithms sub-optimal under the general non-stationary distribution setting. In this work, we propose algorithms that utilize the variance of the reward distribution as well as the $B_K$, and show that they can achieve tighter regret upper bounds. Specifically, we introduce two novel algorithms: Restarted Weighted$\text{OFUL}^+$ and Restarted $\text{SAVE}^+$. These algorithms address cases where the variance information of the rewards is known and unknown, respectively. Notably, when the total variance $V_K$ is much smaller than $K$, our algorithms outperform previous state-of-the-art results on non-stationary stochastic linear bandits under different settings. Experimental evaluations further validate the superior performance of our proposed algorithms over existing works.

In this paper we study the non-stationary stochastic optimization question with bandit feedback and dynamic regret measures. The seminal work of Besbes et al. (2015) shows that, when aggregated function changes is known a priori, a simple re-starting algorithm attains the optimal dynamic regret. In this work, we designed a stochastic optimization algorithm with fixed step sizes, which combined together with the multi-scale sampling framework of Wei and Luo (2021) achieves the optimal dynamic regret in non-stationary stochastic optimization without requiring prior knowledge of function change budget, thereby closes a question that has been open for a while. We also establish an additional result showing that any algorithm achieving good regret against stationary benchmarks with high probability could be automatically converted to an algorithm that achieves good regret against dynamic benchmarks, which is applicable to a wide class of bandit convex optimization algorithms.