Handling the problem of scalability is one of the essential issues for multi-agent reinforcement learning (MARL) algorithms to be applied to real-world problems typically involving massively many agents. For this, parameter sharing across multiple agents has widely been used since it reduces the training time by decreasing the number of parameters and increasing the sample efficiency. However, using the same parameters across agents limits the representational capacity of the joint policy and consequently, the performance can be degraded in multi-agent tasks that require different behaviors for different agents. In this paper, we propose a simple method that adopts structured pruning for a deep neural network to increase the representational capacity of the joint policy without introducing additional parameters. We evaluate the proposed method on several benchmark tasks, and numerical results show that the proposed method significantly outperforms other parameter-sharing methods.

In robust Markov decision processes (MDPs), the uncertainty in the transition kernel is addressed by finding a policy that optimizes the worst-case performance over an uncertainty set of MDPs. While much of the literature has focused on discounted MDPs, robust average-reward MDPs remain largely unexplored. In this paper, we focus on robust average-reward MDPs, where the goal is to find a policy that optimizes the worst-case average reward over an uncertainty set. We first take an approach that approximates average-reward MDPs using discounted MDPs. We prove that the robust discounted value function converges to the robust average-reward as the discount factor $\gamma$ goes to $1$, and moreover, when $\gamma$ is large, any optimal policy of the robust discounted MDP is also an optimal policy of the robust average-reward. We further design a robust dynamic programming approach, and theoretically characterize its convergence to the optimum. Then, we investigate robust average-reward MDPs directly without using discounted MDPs as an intermediate step. We derive the robust Bellman equation for robust average-reward MDPs, prove that the optimal policy can be derived from its solution, and further design a robust relative value iteration algorithm that provably finds its solution, or equivalently, the optimal robust policy.

Offline reinforcement learning (RL) aims at learning an optimal strategy using a pre-collected dataset without further interactions with the environment. While various algorithms have been proposed for offline RL in the previous literature, the minimax optimality has only been (nearly) established for tabular Markov decision processes (MDPs). In this paper, we focus on offline RL with linear function approximation and propose a new pessimism-based algorithm for offline linear MDP. At the core of our algorithm is the uncertainty decomposition via a reference function, which is new in the literature of offline RL under linear function approximation. Theoretical analysis demonstrates that our algorithm can match the performance lower bound up to logarithmic factors. We also extend our techniques to the two-player zero-sum Markov games (MGs), and establish a new performance lower bound for MGs, which tightens the existing result, and verifies the nearly minimax optimality of the proposed algorithm. To the best of our knowledge, these are the first computationally efficient and nearly minimax optimal algorithms for offline single-agent MDPs and MGs with linear function approximation.

A zero-shot RL agent is an agent that can solve any RL task in a given environment, instantly with no additional planning or learning, after an initial reward-free learning phase. This marks a shift from the reward-centric RL paradigm towards "controllable" agents that can follow arbitrary instructions in an environment. Current RL agents can solve families of related tasks at best, or require planning anew for each task. Strategies for approximate zero-shot RL ave been suggested using successor features (SFs) [BBQ+ 18] or forward-backward (FB) representations [TO21], but testing has been limited. After clarifying the relationships between these schemes, we introduce improved losses and new SF models, and test the viability of zero-shot RL schemes systematically on tasks from the Unsupervised RL benchmark [LYL+21]. To disentangle universal representation learning from exploration, we work in an offline setting and repeat the tests on several existing replay buffers. SFs appear to suffer from the choice of the elementary state features. SFs with Laplacian eigenfunctions do well, while SFs based on auto-encoders, inverse curiosity, transition models, low-rank transition matrix, contrastive learning, or diversity (APS), perform unconsistently. In contrast, FB representations jointly learn the elementary and successor features from a single, principled criterion. They perform best and consistently across the board, reaching 85% of supervised RL performance with a good replay buffer, in a zero-shot manner.

Although parallelism has been extensively used in reinforcement learning (RL), the quantitative effects of parallel exploration are not well understood theoretically. We study the benefits of simple parallel exploration for reward-free RL in linear Markov decision processes (MDPs) and two-player zero-sum Markov games (MGs). In contrast to the existing literature, which focuses on approaches that encourage agents to explore a diverse set of policies, we show that using a single policy to guide exploration across all agents is sufficient to obtain an almost-linear speedup in all cases compared to their fully sequential counterpart. Furthermore, we demonstrate that this simple procedure is near-minimax optimal in the reward-free setting for linear MDPs. From a practical perspective, our paper shows that a single policy is sufficient and provably near-optimal for incorporating parallelism during the exploration phase.

Deep reinforcement learning agents are notoriously sample inefficient, which considerably limits their application to real-world problems. Recently, many model-based methods have been designed to address this issue, with learning in the imagination of a world model being one of the most prominent approaches. However, while virtually unlimited interaction with a simulated environment sounds appealing, the world model has to be accurate over extended periods of time. Motivated by the success of Transformers in sequence modeling tasks, we introduce IRIS, a data-efficient agent that learns in a world model composed of a discrete autoencoder and an autoregressive Transformer. With the equivalent of only two hours of gameplay in the Atari 100k benchmark, IRIS achieves a mean human normalized score of 1.046, and outperforms humans on 10 out of 26 games, setting a new state of the art for methods without lookahead search. To foster future research on Transformers and world models for sample-efficient reinforcement learning, we release our code and models at https://github.com/eloialonso/iris.

The rapid changes in the finance industry due to the increasing amount of data have revolutionized the techniques on data processing and data analysis and brought new theoretical and computational challenges. In contrast to classical stochastic control theory and other analytical approaches for solving financial decision-making problems that heavily reply on model assumptions, new developments from reinforcement learning (RL) are able to make full use of the large amount of financial data with fewer model assumptions and to improve decisions in complex financial environments. This survey paper aims to review the recent developments and use of RL approaches in finance. We give an introduction to Markov decision processes, which is the setting for many of the commonly used RL approaches. Various algorithms are then introduced with a focus on value and policy based methods that do not require any model assumptions. Connections are made with neural networks to extend the framework to encompass deep RL algorithms. Our survey concludes by discussing the application of these RL algorithms in a variety of decision-making problems in finance, including optimal execution, portfolio optimization, option pricing and hedging, market making, smart order routing, and robo-advising.

While deep reinforcement learning (RL) is becoming an integral part of good decision-making in data science, it is still plagued with sample inefficiency. This can be challenging when applying deep-RL in real-world environments where physical interactions are expensive and can risk system safety. To improve the sample efficiency of RL algorithms, this paper proposes a novel human-inspired framework that facilitates fast exploration and learning for difficult RL tasks. The main idea is to first provide the learning agent with simpler but similar tasks that gradually grow in difficulty and progress toward the main task. The proposed method requires no pre-training phase. Specifically, the learning of simpler tasks is only done for one iteration. The generated knowledge could be used by any transfer learning, including value transfer and policy transfer, to reduce the sample complexity while not adding to the computational complexity. So, it can be applied to any goal, environment, and reinforcement learning algorithm - both value-based methods and policy-based methods and both tabular methods and deep-RL methods. We have evaluated our proposed framework on both a simple Random Walk for illustration purposes and on more challenging optimal control problems with constraint. The experiments show the good performance of our proposed framework in improving the sample efficiency of RL-learning algorithms, especially when the main task is difficult.

Hierarchical Reinforcement Learning (HRL) agents have the potential to demonstrate appealing capabilities such as planning and exploration with abstraction, transfer, and skill reuse. Recent successes with HRL across different domains provide evidence that practical, effective HRL agents are possible, even if existing agents do not yet fully realize the potential of HRL. Despite these successes, visually complex partially observable 3D environments remained a challenge for HRL agents. We address this issue with Hierarchical Hybrid Offline-Online (H2O2), a hierarchical deep reinforcement learning agent that discovers and learns to use options from scratch using its own experience. We show that H2O2 is competitive with a strong non-hierarchical Muesli baseline in the DeepMind Hard Eight tasks and we shed new light on the problem of learning hierarchical agents in complex environments. Our empirical study of H2O2 reveals previously unnoticed practical challenges and brings new perspective to the current understanding of hierarchical agents in complex domains.

We study the problem of planning restless multi-armed bandits (RMABs) with multiple actions. This is a popular model for multi-agent systems with applications like multi-channel communication, monitoring and machine maintenance tasks, and healthcare. Whittle index policies, which are based on Lagrangian relaxations, are widely used in these settings due to their simplicity and near-optimality under certain conditions. In this work, we first show that Whittle index policies can fail in simple and practically relevant RMAB settings, even when the RMABs are indexable. We discuss why the optimality guarantees fail and why asymptotic optimality may not translate well to practically relevant planning horizons. We then propose an alternate planning algorithm based on the mean-field method, which can provably and efficiently obtain near-optimal policies with a large number of arms, without the stringent structural assumptions required by the Whittle index policies. This borrows ideas from existing research with some improvements: our approach is hyper-parameter free, and we provide an improved non-asymptotic analysis which has: (a) no requirement for exogenous hyper-parameters and tighter polynomial dependence on known problem parameters; (b) high probability bounds which show that the reward of the policy is reliable; and (c) matching sub-optimality lower bounds for this algorithm with respect to the number of arms, thus demonstrating the tightness of our bounds. Our extensive experimental analysis shows that the mean-field approach matches or outperforms other baselines.