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Abstract:Decision Transformer (DT) has emerged as a promising class of algorithms in offline reinforcement learning (RL) tasks, leveraging pre-collected datasets and Transformer's capability to model long sequences. Recent works have demonstrated that using parts of trajectories from training tasks as prompts in DT enhances its performance on unseen tasks, giving rise to Prompt-DT methods. However, collecting data from specific environments can be both costly and unsafe in many scenarios, leading to suboptimal performance and limited few-shot prompt abilities due to the data-hungry nature of Transformer-based models. Additionally, the limited datasets used in pre-training make it challenging for Prompt-DT type of methods to distinguish between various RL tasks through prompts alone. To address these challenges, we introduce the Language model-initialized Prompt Decision Transformer (LPDT), which leverages pre-trained language models for meta-RL tasks and fine-tunes the model using Low-rank Adaptation (LoRA). We further incorporate prompt regularization to effectively differentiate between tasks based on prompt feature representations. Our approach integrates pre-trained language model and RL tasks seamlessly. Extensive empirical studies demonstrate that initializing with a pre-trained language model significantly enhances the performance of Prompt-DT on unseen tasks compared to baseline methods.

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Authors:Haque Ishfaq, Yixin Tan, Yu Yang, Qingfeng Lan, Jianfeng Lu, A. Rupam Mahmood, Doina Precup, Pan Xu

Abstract:Thompson sampling (TS) is one of the most popular exploration techniques in reinforcement learning (RL). However, most TS algorithms with theoretical guarantees are difficult to implement and not generalizable to Deep RL. While the emerging approximate sampling-based exploration schemes are promising, most existing algorithms are specific to linear Markov Decision Processes (MDP) with suboptimal regret bounds, or only use the most basic samplers such as Langevin Monte Carlo. In this work, we propose an algorithmic framework that incorporates different approximate sampling methods with the recently proposed Feel-Good Thompson Sampling (FGTS) approach (Zhang, 2022; Dann et al., 2021), which was previously known to be computationally intractable in general. When applied to linear MDPs, our regret analysis yields the best known dependency of regret on dimensionality, surpassing existing randomized algorithms. Additionally, we provide explicit sampling complexity for each employed sampler. Empirically, we show that in tasks where deep exploration is necessary, our proposed algorithms that combine FGTS and approximate sampling perform significantly better compared to other strong baselines. On several challenging games from the Atari 57 suite, our algorithms achieve performance that is either better than or on par with other strong baselines from the deep RL literature.

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Abstract:We introduce the E$^4$ algorithm for the batched linear bandit problem, incorporating an Explore-Estimate-Eliminate-Exploit framework. With a proper choice of exploration rate, we prove E$^4$ achieves the finite-time minimax optimal regret with only $O(\log\log T)$ batches, and the asymptotically optimal regret with only $3$ batches as $T\rightarrow\infty$, where $T$ is the time horizon. We further prove a lower bound on the batch complexity of linear contextual bandits showing that any asymptotically optimal algorithm must require at least $3$ batches in expectation as $T\rightarrow\infty$, which indicates E$^4$ achieves the asymptotic optimality in regret and batch complexity simultaneously. To the best of our knowledge, E$^4$ is the first algorithm for linear bandits that simultaneously achieves the minimax and asymptotic optimality in regret with the corresponding optimal batch complexities. In addition, we show that with another choice of exploration rate E$^4$ achieves an instance-dependent regret bound requiring at most $O(\log T)$ batches, and maintains the minimax optimality and asymptotic optimality. We conduct thorough experiments to evaluate our algorithm on randomly generated instances and the challenging \textit{End of Optimism} instances \citep{lattimore2017end} which were shown to be hard to learn for optimism based algorithms. Empirical results show that E$^4$ consistently outperforms baseline algorithms with respect to regret minimization, batch complexity, and computational efficiency.

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Abstract:We present the first study on provably efficient randomized exploration in cooperative multi-agent reinforcement learning (MARL). We propose a unified algorithm framework for randomized exploration in parallel Markov Decision Processes (MDPs), and two Thompson Sampling (TS)-type algorithms, CoopTS-PHE and CoopTS-LMC, incorporating the perturbed-history exploration (PHE) strategy and the Langevin Monte Carlo exploration (LMC) strategy respectively, which are flexible in design and easy to implement in practice. For a special class of parallel MDPs where the transition is (approximately) linear, we theoretically prove that both CoopTS-PHE and CoopTS-LMC achieve a $\widetilde{\mathcal{O}}(d^{3/2}H^2\sqrt{MK})$ regret bound with communication complexity $\widetilde{\mathcal{O}}(dHM^2)$, where $d$ is the feature dimension, $H$ is the horizon length, $M$ is the number of agents, and $K$ is the number of episodes. This is the first theoretical result for randomized exploration in cooperative MARL. We evaluate our proposed method on multiple parallel RL environments, including a deep exploration problem (\textit{i.e.,} $N$-chain), a video game, and a real-world problem in energy systems. Our experimental results support that our framework can achieve better performance, even under conditions of misspecified transition models. Additionally, we establish a connection between our unified framework and the practical application of federated learning.

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Abstract:Distributionally robust offline reinforcement learning (RL), which seeks robust policy training against environment perturbation by modeling dynamics uncertainty, calls for function approximations when facing large state-action spaces. However, the consideration of dynamics uncertainty introduces essential nonlinearity and computational burden, posing unique challenges for analyzing and practically employing function approximation. Focusing on a basic setting where the nominal model and perturbed models are linearly parameterized, we propose minimax optimal and computationally efficient algorithms realizing function approximation and initiate the study on instance-dependent suboptimality analysis in the context of robust offline RL. Our results uncover that function approximation in robust offline RL is essentially distinct from and probably harder than that in standard offline RL. Our algorithms and theoretical results crucially depend on a variety of new techniques, involving a novel function approximation mechanism incorporating variance information, a new procedure of suboptimality and estimation uncertainty decomposition, a quantification of the robust value function shrinkage, and a meticulously designed family of hard instances, which might be of independent interest.

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Abstract:We study off-dynamics Reinforcement Learning (RL), where the policy is trained on a source domain and deployed to a distinct target domain. We aim to solve this problem via online distributionally robust Markov decision processes (DRMDPs), where the learning algorithm actively interacts with the source domain while seeking the optimal performance under the worst possible dynamics that is within an uncertainty set of the source domain's transition kernel. We provide the first study on online DRMDPs with function approximation for off-dynamics RL. We find that DRMDPs' dual formulation can induce nonlinearity, even when the nominal transition kernel is linear, leading to error propagation. By designing a $d$-rectangular uncertainty set using the total variation distance, we remove this additional nonlinearity and bypass the error propagation. We then introduce DR-LSVI-UCB, the first provably efficient online DRMDP algorithm for off-dynamics RL with function approximation, and establish a polynomial suboptimality bound that is independent of the state and action space sizes. Our work makes the first step towards a deeper understanding of the provable efficiency of online DRMDPs with linear function approximation. Finally, we substantiate the performance and robustness of DR-LSVI-UCB through different numerical experiments.

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Abstract:We study the multi-agent multi-armed bandit (MAMAB) problem, where $m$ agents are factored into $\rho$ overlapping groups. Each group represents a hyperedge, forming a hypergraph over the agents. At each round of interaction, the learner pulls a joint arm (composed of individual arms for each agent) and receives a reward according to the hypergraph structure. Specifically, we assume there is a local reward for each hyperedge, and the reward of the joint arm is the sum of these local rewards. Previous work introduced the multi-agent Thompson sampling (MATS) algorithm \citep{verstraeten2020multiagent} and derived a Bayesian regret bound. However, it remains an open problem how to derive a frequentist regret bound for Thompson sampling in this multi-agent setting. To address these issues, we propose an efficient variant of MATS, the $\epsilon$-exploring Multi-Agent Thompson Sampling ($\epsilon$-MATS) algorithm, which performs MATS exploration with probability $\epsilon$ while adopts a greedy policy otherwise. We prove that $\epsilon$-MATS achieves a worst-case frequentist regret bound that is sublinear in both the time horizon and the local arm size. We also derive a lower bound for this setting, which implies our frequentist regret upper bound is optimal up to constant and logarithm terms, when the hypergraph is sufficiently sparse. Thorough experiments on standard MAMAB problems demonstrate the superior performance and the improved computational efficiency of $\epsilon$-MATS compared with existing algorithms in the same setting.

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Abstract:signSGD is popular in nonconvex optimization due to its communication efficiency. Yet, existing analyses of signSGD rely on assuming that data are sampled with replacement in each iteration, contradicting the practical implementation where data are randomly reshuffled and sequentially fed into the algorithm. We bridge this gap by proving the first convergence result of signSGD with random reshuffling (SignRR) for nonconvex optimization. Given the dataset size $n$, the number of epochs of data passes $T$, and the variance bound of a stochastic gradient $\sigma^2$, we show that SignRR has the same convergence rate $O(\log(nT)/\sqrt{nT} + \|\sigma\|_1)$ as signSGD \citep{bernstein2018signsgd}. We then present SignRVR and SignRVM, which leverage variance-reduced gradients and momentum updates respectively, both converging at $O(\log(nT)/\sqrt{nT})$. In contrast with the analysis of signSGD, our results do not require an extremely large batch size in each iteration to be of the same order as the total number of iterations \citep{bernstein2018signsgd} or the signs of stochastic and true gradients match element-wise with a minimum probability of 1/2 \citep{safaryan2021stochastic}. We also extend our algorithms to cases where data are distributed across different machines, yielding dist-SignRVR and dist-SignRVM, both converging at $O(\log(n_0T)/\sqrt{n_0T})$, where $n_0$ is the dataset size of a single machine. We back up our theoretical findings through experiments on simulated and real-world problems, verifying that randomly reshuffled sign methods match or surpass existing baselines.

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Abstract:We study the batched best arm identification (BBAI) problem, where the learner's goal is to identify the best arm while switching the policy as less as possible. In particular, we aim to find the best arm with probability $1-\delta$ for some small constant $\delta>0$ while minimizing both the sample complexity (total number of arm pulls) and the batch complexity (total number of batches). We propose the three-batch best arm identification (Tri-BBAI) algorithm, which is the first batched algorithm that achieves the optimal sample complexity in the asymptotic setting (i.e., $\delta\rightarrow 0$) and runs only in at most $3$ batches. Based on Tri-BBAI, we further propose the almost optimal batched best arm identification (Opt-BBAI) algorithm, which is the first algorithm that achieves the near-optimal sample and batch complexity in the non-asymptotic setting (i.e., $\delta>0$ is arbitrarily fixed), while enjoying the same batch and sample complexity as Tri-BBAI when $\delta$ tends to zero. Moreover, in the non-asymptotic setting, the complexity of previous batch algorithms is usually conditioned on the event that the best arm is returned (with a probability of at least $1-\delta$), which is potentially unbounded in cases where a sub-optimal arm is returned. In contrast, the complexity of Opt-BBAI does not rely on such an event. This is achieved through a novel procedure that we design for checking whether the best arm is eliminated, which is of independent interest.

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Abstract:Off-policy evaluation and learning are concerned with assessing a given policy and learning an optimal policy from offline data without direct interaction with the environment. Often, the environment in which the data are collected differs from the environment in which the learned policy is applied. To account for the effect of different environments during learning and execution, distributionally robust optimization (DRO) methods have been developed that compute worst-case bounds on the policy values assuming that the distribution of the new environment lies within an uncertainty set. Typically, this uncertainty set is defined based on the KL divergence around the empirical distribution computed from the logging dataset. However, the KL uncertainty set fails to encompass distributions with varying support and lacks awareness of the geometry of the distribution support. As a result, KL approaches fall short in addressing practical environment mismatches and lead to over-fitting to worst-case scenarios. To overcome these limitations, we propose a novel DRO approach that employs the Wasserstein distance instead. While Wasserstein DRO is generally computationally more expensive compared to KL DRO, we present a regularized method and a practical (biased) stochastic gradient descent method to optimize the policy efficiently. We also provide a theoretical analysis of the finite sample complexity and iteration complexity for our proposed method. We further validate our approach using a public dataset that was recorded in a randomized stoke trial.

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