Scaling Distributed Multi-task Reinforcement Learning with Experience Sharing

Recently, DARPA launched the ShELL program, which aims to explore how experience sharing can benefit distributed lifelong learning agents in adapting to new challenges. In this paper, we address this issue by conducting both theoretical and empirical research on distributed multi-task reinforcement learning (RL), where a group of $N$ agents collaboratively solves $M$ tasks without prior knowledge of their identities. We approach the problem by formulating it as linearly parameterized contextual Markov decision processes (MDPs), where each task is represented by a context that specifies the transition dynamics and rewards. To tackle this problem, we propose an algorithm called DistMT-LSVI. First, the agents identify the tasks, and then they exchange information through a central server to derive $\epsilon$-optimal policies for the tasks. Our research demonstrates that to achieve $\epsilon$-optimal policies for all $M$ tasks, a single agent using DistMT-LSVI needs to run a total number of episodes that is at most $\tilde{\mathcal{O}}({d^3H^6(\epsilon^{-2}+c_{\rm sep}^{-2})}\cdot M/N)$, where $c_{\rm sep}>0$ is a constant representing task separability, $H$ is the horizon of each episode, and $d$ is the feature dimension of the dynamics and rewards. Notably, DistMT-LSVI improves the sample complexity of non-distributed settings by a factor of $1/N$, as each agent independently learns $\epsilon$-optimal policies for all $M$ tasks using $\tilde{\mathcal{O}}(d^3H^6M\epsilon^{-2})$ episodes. Additionally, we provide numerical experiments conducted on OpenAI Gym Atari environments that validate our theoretical findings.

Tackling Heavy-Tailed Rewards in Reinforcement Learning with Function Approximation: Minimax Optimal and Instance-Dependent Regret Bounds

While numerous works have focused on devising efficient algorithms for reinforcement learning (RL) with uniformly bounded rewards, it remains an open question whether sample or time-efficient algorithms for RL with large state-action space exist when the rewards are \emph{heavy-tailed}, i.e., with only finite $(1+\epsilon)$-th moments for some $\epsilon\in(0,1]$. In this work, we address the challenge of such rewards in RL with linear function approximation. We first design an algorithm, \textsc{Heavy-OFUL}, for heavy-tailed linear bandits, achieving an \emph{instance-dependent} $T$-round regret of $\tilde{O}\big(d T^{\frac{1-\epsilon}{2(1+\epsilon)}} \sqrt{\sum_{t=1}^T \nu_t^2} + d T^{\frac{1-\epsilon}{2(1+\epsilon)}}\big)$, the \emph{first} of this kind. Here, $d$ is the feature dimension, and $\nu_t^{1+\epsilon}$ is the $(1+\epsilon)$-th central moment of the reward at the $t$-th round. We further show the above bound is minimax optimal when applied to the worst-case instances in stochastic and deterministic linear bandits. We then extend this algorithm to the RL settings with linear function approximation. Our algorithm, termed as \textsc{Heavy-LSVI-UCB}, achieves the \emph{first} computationally efficient \emph{instance-dependent} $K$-episode regret of $\tilde{O}(d \sqrt{H \mathcal{U}^*} K^\frac{1}{1+\epsilon} + d \sqrt{H \mathcal{V}^* K})$. Here, $H$ is length of the episode, and $\mathcal{U}^*, \mathcal{V}^*$ are instance-dependent quantities scaling with the central moment of reward and value functions, respectively. We also provide a matching minimax lower bound $\Omega(d H K^{\frac{1}{1+\epsilon}} + d \sqrt{H^3 K})$ to demonstrate the optimality of our algorithm in the worst case. Our result is achieved via a novel robust self-normalized concentration inequality that may be of independent interest in handling heavy-tailed noise in general online regression problems.

MetaVL: Transferring In-Context Learning Ability From Language Models to Vision-Language Models

Large-scale language models have shown the ability to adapt to a new task via conditioning on a few demonstrations (i.e., in-context learning). However, in the vision-language domain, most large-scale pre-trained vision-language (VL) models do not possess the ability to conduct in-context learning. How can we enable in-context learning for VL models? In this paper, we study an interesting hypothesis: can we transfer the in-context learning ability from the language domain to VL domain? Specifically, we first meta-trains a language model to perform in-context learning on NLP tasks (as in MetaICL); then we transfer this model to perform VL tasks by attaching a visual encoder. Our experiments suggest that indeed in-context learning ability can be transferred cross modalities: our model considerably improves the in-context learning capability on VL tasks and can even compensate for the size of the model significantly. On VQA, OK-VQA, and GQA, our method could outperform the baseline model while having 20 times fewer parameters.

Replicability in Reinforcement Learning

We initiate the mathematical study of replicability as an algorithmic property in the context of reinforcement learning (RL). We focus on the fundamental setting of discounted tabular MDPs with access to a generative model. Inspired by Impagliazzo et al. [2022], we say that an RL algorithm is replicable if, with high probability, it outputs the exact same policy after two executions on i.i.d. samples drawn from the generator when its internal randomness is the same. We first provide an efficient $\rho$-replicable algorithm for $(\varepsilon, \delta)$-optimal policy estimation with sample and time complexity $\widetilde O\left(\frac{N^3\cdot\log(1/\delta)}{(1-\gamma)^5\cdot\varepsilon^2\cdot\rho^2}\right)$, where $N$ is the number of state-action pairs. Next, for the subclass of deterministic algorithms, we provide a lower bound of order $\Omega\left(\frac{N^3}{(1-\gamma)^3\cdot\varepsilon^2\cdot\rho^2}\right)$. Then, we study a relaxed version of replicability proposed by Kalavasis et al. [2023] called TV indistinguishability. We design a computationally efficient TV indistinguishable algorithm for policy estimation whose sample complexity is $\widetilde O\left(\frac{N^2\cdot\log(1/\delta)}{(1-\gamma)^5\cdot\varepsilon^2\cdot\rho^2}\right)$. At the cost of $\exp(N)$ running time, we transform these TV indistinguishable algorithms to $\rho$-replicable ones without increasing their sample complexity. Finally, we introduce the notion of approximate-replicability where we only require that two outputted policies are close under an appropriate statistical divergence (e.g., Renyi) and show an improved sample complexity of $\widetilde O\left(\frac{N\cdot\log(1/\delta)}{(1-\gamma)^5\cdot\varepsilon^2\cdot\rho^2}\right)$.

Provably Feedback-Efficient Reinforcement Learning via Active Reward Learning

An appropriate reward function is of paramount importance in specifying a task in reinforcement learning (RL). Yet, it is known to be extremely challenging in practice to design a correct reward function for even simple tasks. Human-in-the-loop (HiL) RL allows humans to communicate complex goals to the RL agent by providing various types of feedback. However, despite achieving great empirical successes, HiL RL usually requires too much feedback from a human teacher and also suffers from insufficient theoretical understanding. In this paper, we focus on addressing this issue from a theoretical perspective, aiming to provide provably feedback-efficient algorithmic frameworks that take human-in-the-loop to specify rewards of given tasks. We provide an active-learning-based RL algorithm that first explores the environment without specifying a reward function and then asks a human teacher for only a few queries about the rewards of a task at some state-action pairs. After that, the algorithm guarantees to provide a nearly optimal policy for the task with high probability. We show that, even with the presence of random noise in the feedback, the algorithm only takes $\widetilde{O}(H{{\dim_{R}^2}})$ queries on the reward function to provide an $\epsilon$-optimal policy for any $\epsilon > 0$. Here $H$ is the horizon of the RL environment, and $\dim_{R}$ specifies the complexity of the function class representing the reward function. In contrast, standard RL algorithms require to query the reward function for at least $\Omega(\operatorname{poly}(d, 1/\epsilon))$ state-action pairs where $d$ depends on the complexity of the environmental transition.

Does Sparsity Help in Learning Misspecified Linear Bandits?

Recently, the study of linear misspecified bandits has generated intriguing implications of the hardness of learning in bandits and reinforcement learning (RL). In particular, Du et al. (2020) show that even if a learner is given linear features in $\mathbb{R}^d$ that approximate the rewards in a bandit or RL with a uniform error of $\varepsilon$, searching for an $O(\varepsilon)$-optimal action requires pulling at least $\Omega(\exp(d))$ queries. Furthermore, Lattimore et al. (2020) show that a degraded $O(\varepsilon\sqrt{d})$-optimal solution can be learned within $\operatorname{poly}(d/\varepsilon)$ queries. Yet it is unknown whether a structural assumption on the ground-truth parameter, such as sparsity, could break the $\varepsilon\sqrt{d}$ barrier. In this paper, we address this question by showing that algorithms can obtain $O(\varepsilon)$-optimal actions by querying $O(\varepsilon^{-s}d^s)$ actions, where $s$ is the sparsity parameter, removing the $\exp(d)$-dependence. We then establish information-theoretical lower bounds, i.e., $\Omega(\exp(s))$, to show that our upper bound on sample complexity is nearly tight if one demands an error $ O(s^{\delta}\varepsilon)$ for $0<\delta<1$. For $\delta\geq 1$, we further show that $\operatorname{poly}(s/\varepsilon)$ queries are possible when the linear features are "good" and even in general settings. These results provide a nearly complete picture of how sparsity can help in misspecified bandit learning and provide a deeper understanding of when linear features are "useful" for bandit and reinforcement learning with misspecification.

Near Sample-Optimal Reduction-based Policy Learning for Average Reward MDP

This work considers the sample complexity of obtaining an $\varepsilon$-optimal policy in an average reward Markov Decision Process (AMDP), given access to a generative model (simulator). When the ground-truth MDP is weakly communicating, we prove an upper bound of $\widetilde O(H \varepsilon^{-3} \ln \frac{1}{\delta})$ samples per state-action pair, where $H := sp(h^*)$ is the span of bias of any optimal policy, $\varepsilon$ is the accuracy and $\delta$ is the failure probability. This bound improves the best-known mixing-time-based approaches in [Jin & Sidford 2021], which assume the mixing-time of every deterministic policy is bounded. The core of our analysis is a proper reduction bound from AMDP problems to discounted MDP (DMDP) problems, which may be of independent interests since it allows the application of DMDP algorithms for AMDP in other settings. We complement our upper bound by proving a minimax lower bound of $\Omega(|\mathcal S| |\mathcal A| H \varepsilon^{-2} \ln \frac{1}{\delta})$ total samples, showing that a linear dependent on $H$ is necessary and that our upper bound matches the lower bound in all parameters of $(|\mathcal S|, |\mathcal A|, H, \ln \frac{1}{\delta})$ up to some logarithmic factors.

Contexts can be Cheap: Solving Stochastic Contextual Bandits with Linear Bandit Algorithms

In this paper, we address the stochastic contextual linear bandit problem, where a decision maker is provided a context (a random set of actions drawn from a distribution). The expected reward of each action is specified by the inner product of the action and an unknown parameter. The goal is to design an algorithm that learns to play as close as possible to the unknown optimal policy after a number of action plays. This problem is considered more challenging than the linear bandit problem, which can be viewed as a contextual bandit problem with a \emph{fixed} context. Surprisingly, in this paper, we show that the stochastic contextual problem can be solved as if it is a linear bandit problem. In particular, we establish a novel reduction framework that converts every stochastic contextual linear bandit instance to a linear bandit instance, when the context distribution is known. When the context distribution is unknown, we establish an algorithm that reduces the stochastic contextual instance to a sequence of linear bandit instances with small misspecifications and achieves nearly the same worst-case regret bound as the algorithm that solves the misspecified linear bandit instances. As a consequence, our results imply a $O(d\sqrt{T\log T})$ high-probability regret bound for contextual linear bandits, making progress in resolving an open problem in (Li et al., 2019), (Li et al., 2021). Our reduction framework opens up a new way to approach stochastic contextual linear bandit problems, and enables improved regret bounds in a number of instances including the batch setting, contextual bandits with misspecifications, contextual bandits with sparse unknown parameters, and contextual bandits with adversarial corruption.

Near-Optimal Sample Complexity Bounds for Constrained MDPs

In contrast to the advances in characterizing the sample complexity for solving Markov decision processes (MDPs), the optimal statistical complexity for solving constrained MDPs (CMDPs) remains unknown. We resolve this question by providing minimax upper and lower bounds on the sample complexity for learning near-optimal policies in a discounted CMDP with access to a generative model (simulator). In particular, we design a model-based algorithm that addresses two settings: (i) relaxed feasibility, where small constraint violations are allowed, and (ii) strict feasibility, where the output policy is required to satisfy the constraint. For (i), we prove that our algorithm returns an $\epsilon$-optimal policy with probability $1 - \delta$, by making $\tilde{O}\left(\frac{S A \log(1/\delta)}{(1 - \gamma)^3 \epsilon^2}\right)$ queries to the generative model, thus matching the sample-complexity for unconstrained MDPs. For (ii), we show that the algorithm's sample complexity is upper-bounded by $\tilde{O} \left(\frac{S A \, \log(1/\delta)}{(1 - \gamma)^5 \, \epsilon^2 \zeta^2} \right)$ where $\zeta$ is the problem-dependent Slater constant that characterizes the size of the feasible region. Finally, we prove a matching lower-bound for the strict feasibility setting, thus obtaining the first near minimax optimal bounds for discounted CMDPs. Our results show that learning CMDPs is as easy as MDPs when small constraint violations are allowed, but inherently more difficult when we demand zero constraint violation.

Learning in Distributed Contextual Linear Bandits Without Sharing the Context

Contextual linear bandits is a rich and theoretically important model that has many practical applications. Recently, this setup gained a lot of interest in applications over wireless where communication constraints can be a performance bottleneck, especially when the contexts come from a large $d$-dimensional space. In this paper, we consider a distributed memoryless contextual linear bandit learning problem, where the agents who observe the contexts and take actions are geographically separated from the learner who performs the learning while not seeing the contexts. We assume that contexts are generated from a distribution and propose a method that uses $\approx 5d$ bits per context for the case of unknown context distribution and $0$ bits per context if the context distribution is known, while achieving nearly the same regret bound as if the contexts were directly observable. The former bound improves upon existing bounds by a $\log(T)$ factor, where $T$ is the length of the horizon, while the latter achieves information theoretical tightness.