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Multi-agent reinforcement learning (MARL) lies at the heart of a plethora of applications involving the interaction of a group of agents in a shared unknown environment. A prominent framework for studying MARL is Markov games, with the goal of finding various notions of equilibria in a sample-efficient manner, such as the Nash equilibrium (NE) and the coarse correlated equilibrium (CCE). However, existing sample-efficient approaches either require tailored uncertainty estimation under function approximation, or careful coordination of the players. In this paper, we propose a novel model-based algorithm, called VMG, that incentivizes exploration via biasing the empirical estimate of the model parameters towards those with a higher collective best-response values of all the players when fixing the other players’ policies, thus encouraging the policy to deviate from its current equilibrium for more exploration. VMG is oblivious to different forms of function approximation, and permits simultaneous and uncoupled policy updates of all players. Theoretically, we also establish that VMG achieves a near-optimal regret for finding both the NEs of two-player zero-sum Markov games and CCEs of multi-player general-sum Markov games under linear function approximation in an online environment, which nearly match their counterparts with sophisticated uncertainty quantification. 

Diffusion policies have achieved superior performance in imitation learning and offline reinforcement learning (RL) due to their rich expressiveness. However, the conventional diffusion training procedure requires samples from target distribution, which is impossible in online RL since we cannot sample from the optimal policy. Backpropagating policy gradient through the diffusion process incurs huge computational costs and instability, thus being expensive and not scalable. To enable efficient training of diffusion policies in online RL, we generalize the conventional denoising score matching by reweighting the loss function. The resulting Reweighted Score Matching (RSM) preserves the optimal solution and low computational cost of denoising score matching, while eliminating the need to sample from the target distribution and allowing learning to optimize value functions. We introduce two tractable reweighted loss functions to solve two commonly used policy optimization problems, policy mirror descent and max-entropy policy, resulting in two practical algorithms named Diffusion Policy Mirror Descent (DPMD) and Soft Diffusion Actor-Critic (SDAC). We conducted comprehensive comparisons on MuJoCo benchmarks. The empirical results show that the proposed algorithms outperform recent diffusion-policy online RLs on most tasks, and the DPMD improves more than 120% over soft actor-critic on Humanoid and Ant. 

The pursuit of robustness has recently been a popular topic in reinforcement learning (RL) research, yet the existing methods generally suffer from computation issues that obstruct their real-world implementation. In this paper, we consider MDPs with low-rank structures, where the transition kernel can be written as a linear product of feature map and factors. We introduce *duple perturbation* robustness, i.e. perturbation on both the feature map and the factors, via a novel characterization of (𝜉,𝜂) -ambiguity sets featuring computational efficiency. Our novel low-rank robust MDP formulation is compatible with the low-rank function representation view, and therefore, is naturally applicable to practical RL problems with large or even continuous state-action spaces. Meanwhile, it also gives rise to a provably efficient and practical algorithm with theoretical convergence rate guarantee. Lastly, the robustness of our proposed approach is justified by numerical experiments, including classical control tasks with continuous state-action spaces. 

Network Markov Decision Processes (MDPs), which are the de-facto model for multi-agent control, pose a significant challenge to efficient learning caused by the exponential growth of the global state-action space with the number of agents. In this work, utilizing the exponential decay property of network dynamics, we first derive scalable spectral local representations for multiagent reinforcement learning in network MDPs, which induces a network linear subspace for the local $$Q$$-function of each agent. Building on these local spectral representations, we design a scalable algorithmic framework for multiagent reinforcement learning in continuous state-action network MDPs, and provide end-to-end guarantees for the convergence of our algorithm. Empirically, we validate the effectiveness of our scalable representation-based approach on two benchmark problems, and demonstrate the advantages of our approach over generic function approximation approaches to representing the local $$Q$$-functions.