All prior results suffer from at least one of the two obstacles: the curse of multiple agents and the barrier of long horizon, regardless of the sampling protocol in use. We take a step towards settling this problem, assuming access to a flexible sampling mechanism: the generative model. Focusing on non-stationary finite-horizon Markov games, we develop a fast learning algorithm called Q-FTRL and an adaptive sampling scheme that leverage the optimism principle in online adversarial learning (particularly the Follow-the-Regularized-Leader (FTRL) method). Our algorithm learns an $\varepsilon$-approximate CCE in a general-sum Markov game using $$ \widetilde{O}\bigg( \frac{H^4 S \sum_{i=1}^m A_i}{\varepsilon^2} \bigg) $$ samples, where $m$ is the number of players, $S$ indicates the number of states, $H$ is the horizon, and $A_i$ denotes the number of actions for the $i$-th player. This is minimax-optimal (up to log factor) when $m$ is fixed. When applied to two-player zero-sum Markov games, our algorithm provably finds an $\varepsilon$-approximate Nash equilibrium with a minimal number of samples. Along the way, we derive a refined regret bound for FTRL that makes explicit the role of variance-type quantities, which might be of independent interest.

In this paper, we study the problem of networked multi-agent reinforcement learning (MARL), where a number of agents are deployed as a partially connected network and each interacts only with nearby agents. Networked MARL requires all agents to make decisions in a decentralized manner to optimize a global objective with restricted communication between neighbors over the network. Inspired by the fact that sharing plays a key role in human's learning of cooperation, we propose LToS, a hierarchically decentralized MARL framework that enables agents to learn to dynamically share reward with neighbors so as to encourage agents to cooperate on the global objective through collectives. For each agent, the high-level policy learns how to share reward with neighbors to decompose the global objective, while the low-level policy learns to optimize the local objective induced by the high-level policies in the neighborhood. The two policies form a bi-level optimization and learn alternately. We empirically demonstrate that LToS outperforms existing methods in both social dilemma and networked MARL scenarios across scales.

An increasingly common setting in machine learning involves multiple parties, each with their own data, who want to jointly make predictions on future test points. Agents wish to benefit from the collective expertise of the full set of agents to make better predictions than they would individually, but may not be willing to release labeled data or model parameters. In this work, we explore a decentralized mechanism to make collective predictions at test time, that is inspired by the literature in social science on human consensus-making. Building on a query model to facilitate information exchange among agents, our approach leverages each agent's pre-trained model without relying on external validation, model retraining, or data pooling. A theoretical analysis shows that our approach recovers inverse mean-squared-error (MSE) weighting in the large-sample limit which is known to be the optimal way to combine independent, unbiased estimators. Empirically, we demonstrate that our scheme effectively combines models with differing quality across the input space: the proposed consensus prediction achieves significant gains over classical model averaging, and even outperforms weighted averaging schemes that have access to additional validation data. Finally, we propose a decentralized Jackknife procedure as a tool to evaluate the sensitivity of the collective predictions with respect to a single agent's opinion.

Policy gradient (PG) methods are popular reinforcement learning (RL) methods where a baseline is often applied to reduce the variance of gradient estimates. In multi-agent RL (MARL), although the PG theorem can be naturally extended, the effectiveness of multi-agent PG (MAPG) methods degrades as the variance of gradient estimates increases rapidly with the number of agents. In this paper, we offer a rigorous analysis of MAPG methods by, firstly, quantifying the contributions of the number of agents and agents' explorations to the variance of MAPG estimators. Based on this analysis, we derive the optimal baseline (OB) that achieves the minimal variance.

This paper introduces a general multi-agent bandit model in which each agent is facing a finite set of arms and may communicate with other agents through a central controller in order to identify -in pure exploration-or play -in regret minimization-its optimal arm. The twist is that the optimal arm for each agent is the arm with largest expected mixed reward, where the mixed reward of an arm is a weighted sum of the rewards of this arm for all agents. This makes communication between agents often necessary. This general setting allows to recover and extend several recent models for collaborative bandit learning, including the recently proposed federated learning with personalization [Shi et al., 2021]. In this paper, we provide new lower bounds on the sample complexity of pure exploration and on the regret. We then propose a near-optimal algorithm for pure exploration. This algorithm is based on phased elimination with two novel ingredients: a data-dependent sampling scheme within each phase, aimed at matching a relaxation of the lower bound.

Recently, game-playing agents based on AI techniques have demonstrated super-human performance in several sequential games, such as chess, Go, and poker. Surprisingly, the multi-agent learning techniques that allowed to reach these achievements do not take into account the actual behavior of the human player, potentially leading to an impressive gap in performances. In this paper, we address the problem of designing artificial agents that learn how to effectively exploit unknown human opponents while playing repeatedly against them in an online fashion. We study the case in which the agent's strategy during each repetition of the game is subject to constraints ensuring that the human's expected utility is within some lower and upper thresholds. Our framework encompasses several real-world problems, such as human engagement in repeated game playing and human education by means of serious games. As a first result, we formalize a set of linear inequalities encoding the conditions that the agent's strategy must satisfy at each iteration in order to do not violate the given bounds for the human's expected utility. Then, we use such formulation in an upper confidence bound algorithm, and we prove that the resulting procedure suffers from sublinear regret and guarantees that the constraints are satisfied with high probability at each iteration. Finally, we empirically evaluate the convergence of our algorithm on standard testbeds of sequential games.

We present a multi-agent actor-critic method that aims to implicitly address the credit assignment problem under fully cooperative settings. Our key motivation is that credit assignment among agents may not require an explicit formulation as long as (1) the policy gradients derived from a centralized critic carry sufficient information for the decentralized agents to maximize their joint action value through optimal cooperation and (2) a sustained level of exploration is enforced throughout training. Under the centralized training with decentralized execution (CTDE) paradigm, we achieve the former by formulating the centralized critic as a hypernetwork such that a latent state representation is integrated into the policy gradients through its multiplicative association with the stochastic policies; to achieve the latter, we derive a simple technique called adaptive entropy regularization where magnitudes of the entropy gradients are dynamically rescaled based on the current policy stochasticity to encourage consistent levels of exploration. Our algorithm, referred to as LICA, is evaluated on several benchmarks including the multi-agent particle environments and a set of challenging StarCraft II micromanagement tasks, and we show that LICA significantly outperforms previous methods.

We study envy-free policy teaching. A number of agents independently explore a common Markov decision process (MDP), but each with their own reward function and discounting rate. A teacher wants to teach a target policy to this diverse group of agents, by means of modifying the agents' reward functions: providing additional bonuses to certain actions, or penalizing them. When personalized reward modification programs are used, an important question is how to design the programs so that the agents think they are treated fairly. We adopt the notion of envy-freeness (EF) from the literature on fair division to formalize this problem and investigate several fundamental questions about the existence of EF solutions in our setting, the computation of cost-minimizing solutions, as well as the price of fairness (PoF), which measures the increase of cost due to the consideration of fairness. We show that 1) an EF solution may not exist if penalties are not allowed in the modifications, but otherwise always exists.

We propose FACtored Multi-Agent Centralised policy gradients (FACMAC), a new method for cooperative multi-agent reinforcement learning in both discrete and continuous action spaces. Like MADDPG, a popular multi-agent actor-critic method, our approach uses deep deterministic policy gradients to learn policies. However, FACMAC learns a centralised but factored critic, which combines per-agent utilities into the joint action-value function via a non-linear monotonic function, as in QMIX, a popular multi-agent $Q$-learning algorithm. However, unlike QMIX, there are no inherent constraints on factoring the critic. We thus also employ a nonmonotonic factorisation and empirically demonstrate that its increased representational capacity allows it to solve some tasks that cannot be solved with monolithic, or monotonically factored critics. In addition, FACMAC uses a centralised policy gradient estimator that optimises over the entire joint action space, rather than optimising over each agent's action space separately as in MADDPG. This allows for more coordinated policy changes and fully reaps the benefits of a centralised critic. We evaluate FACMAC on variants of the multi-agent particle environments, a novel multi-agent MuJoCo benchmark, and a challenging set of StarCraft II micromanagement tasks. Empirical results demonstrate FACMAC's superior performance over MADDPG and other baselines on all three domains.

Multi-agent control is a central theme in the Cyber-Physical Systems (CPS). However, current control methods either receive non-Markovian states due to insufficient sensing and decentralized design, or suffer from poor convergence. This paper presents the Delayed Propagation Transformer (DePT), a new transformer-based model that specializes in the global modeling of CPS while taking into account the immutable constraints from the physical world. DePT induces a cone-shaped spatial-temporal attention prior, which injects the information propagation and aggregation principles and enables a global view. With physical constraint inductive bias baked into its design, our DePT is ready to plug and play for a broad class of multi-agent systems. The experimental results on one of the most challenging CPS -- network-scale traffic signal control system in the open world -- show that our model outperformed the state-of-the-art expert methods on synthetic and real-world datasets.