Tingting Ni

Tingting Ni, Anna Maddux, Maryam Kamgarpour

Markov games with coupling constraints model constrained dynamical decision-making involving self-interested agents, where the feasibility of an individual agent's strategy depends on the joint strategies of the others. Such games arise in numerous real-world applications involving safety requirements and budget caps, for example, in environmental management, electricity markets, and transportation systems. In unconstrained dynamical decision-making, the correlated equilibrium has emerged as a desired solution concept due to its computational tractability and amenability to learning algorithms. Understanding how coupling constraints shape correlated equilibria is a crucial step towards computing solutions in constrained Markov games. In this paper, we formalize and characterize the notion of constrained correlated equilibria for Markov games, defined as feasible joint policies where any unilateral deviation is either unprofitable or infeasible. Building on this characterization, we further study existence conditions for constrained correlated equilibria. In particular, we provide a novel existence proof of such equilibria in Markov games with coupling constraints.

Tingting Ni, Maryam Kamgarpour

We develop a model-free approach to optimally control stochastic, Markovian systems subject to a reach-avoid constraint. Specifically, the state trajectory must remain within a safe set while reaching a target set within a finite time horizon. Due to the time-dependent nature of these constraints, we show that, in general, the optimal policy for this constrained stochastic control problem is non-Markovian, which increases the computational complexity. To address this challenge, we apply the state-augmentation technique from arXiv:2402.19360, reformulating the problem as a constrained Markov decision process (CMDP) on an extended state space. This transformation allows us to search for a Markovian policy, avoiding the complexity of non-Markovian policies. To learn the optimal policy without a system model, and using only trajectory data, we develop a log-barrier policy gradient approach. We prove that under suitable assumptions, the policy parameters converge to the optimal parameters, while ensuring that the system trajectories satisfy the stochastic reach-avoid constraint with high probability.

Titouan Renard, Andreas Schlaginhaufen, Tingting Ni et al.

Given a dataset of expert demonstrations, inverse reinforcement learning (IRL) aims to recover a reward for which the expert is optimal. This work proposes a model-free algorithm to solve entropy-regularized IRL problem. In particular, we employ a stochastic gradient descent update for the reward and a stochastic soft policy iteration update for the policy. Assuming access to a generative model, we prove that our algorithm is guaranteed to recover a reward for which the expert is $\varepsilon$-optimal using $\mathcal{O}(1/\varepsilon^{2})$ samples of the Markov decision process (MDP). Furthermore, with $\mathcal{O}(1/\varepsilon^{4})$ samples we prove that the optimal policy corresponding to the recovered reward is $\varepsilon$-close to the expert policy in total variation distance.