Reinforcement learning with general utilities (RLGU) offers a unifying framework to capture several problems beyond standard expected returns, including imitation learning, pure exploration, and safe RL. Despite recent fundamental advances in the theoretical analysis of policy gradient (PG) methods for standard RL and recent efforts in RLGU, the understanding of these PG algorithms and their scope of application in RLGU still remain limited. In this work, we establish global optimality guarantees of PG methods for RLGU in which the objective is a general concave utility function of the state-action occupancy measure. In the tabular setting, we provide global optimality results using a new proof technique building on recent theoretical developments on the convergence of PG methods for standard RL using gradient domination. Our proof technique opens avenues for analyzing policy parameterizations beyond the direct policy parameterization for RLGU. In addition, we provide global optimality results for large state-action space settings beyond prior work which has mostly focused on the tabular setting. In this large scale setting, we adapt PG methods by approximating occupancy measures within a function approximation class using maximum likelihood estimation. Our sample complexity only scales with the dimension induced by our approximation class instead of the size of the state-action space.

TRPO, PPO), and a critic that involves minimizing a closely connected objective.

We present ABIDES-MARL, a framework that combines a new multi-agent reinforcement learning (MARL) methodology with a new realistic limit-order-book (LOB) simulation system to study equilibrium behavior in complex financial market games. The system extends ABIDES-Gym by decoupling state collection from kernel interruption, enabling synchronized learning and decision-making for multiple adaptive agents while maintaining compatibility with standard RL libraries. It preserves key market features such as price-time priority and discrete tick sizes. Methodologically, we use MARL to approximate equilibrium-like behavior in multi-period trading games with a finite number of heterogeneous agents-an informed trader, a liquidity trader, noise traders, and competing market makers-all with individual price impacts. This setting bridges optimal execution and market microstructure by embedding the liquidity trader's optimization problem within a strategic trading environment. We validate the approach by solving an extended Kyle model within the simulation system, recovering the gradual price discovery phenomenon. We then extend the analysis to a liquidity trader's problem where market liquidity arises endogenously and show that, at equilibrium, execution strategies shape market-maker behavior and price dynamics. ABIDES-MARL provides a reproducible foundation for analyzing equilibrium and strategic adaptation in realistic markets and contributes toward building economically interpretable agentic AI systems for finance.

TRPO, PPO), and a critic that involves minimizing a closely connected objective.

It's not clear if there are any other meaningful Theorem 3 doesn't require the policy class The authors should emphasize this. Y es, we agree with reviewer's comment. (Theorem 2). Describe why the paper's approach offers advantages over [18]. See also response to Reviewer #3 (C2).

Abstract-- Multi-agent games in dynamic nonlinear settings are challenging due to the time-varying interactions among the agents and the non-stationarity of the (potential) Nash equilibria. In this paper we consider model-free games, where agent transitions and costs are observed without knowledge of the transition and cost functions that generate them. We propose a policy gradient approach to learn distributed policies that follow the communication structure in multi-team games, with multiple agents per team. Our formulation is inspired by the structure of distributed policies in linear quadratic games, which take the form of time-varying linear feedback gains. In the nonlinear case, we model the policies as nonlinear feedback gains, parameterized by self-attention layers to account for the time-varying multi-agent communication topology. We demonstrate that our distributed policy gradient approach achieves strong performance in several settings, including distributed linear and nonlinear regulation, and simulated and real multi-robot pursuit-and-evasion games.

The proof is similar to the one above for Lemma A.1: Proof.

Learning With Opponent-Learning A wareness (LOLA) (Foerster et al. [2018a]) is a multi-agent reinforcement learning algorithm that typically learns reciprocity-based

We present a data-driven, probabilistic trajectory optimization framework for systems with unknown dynamics, called Probabilistic Differential Dynamic Programming (PDDP). PDDP takes into account uncertainty explicitly for dynamics models using Gaussian processes (GPs). Based on the second-order local approximation of the value function, PDDP performs Dynamic Programming around a nominal trajectory in Gaussian belief spaces. Different from typical gradientbased policy search methods, PDDP does not require a policy parameterization and learns a locally optimal, time-varying control policy. We demonstrate the effectiveness and efficiency of the proposed algorithm using two nontrivial tasks. Compared with the classical DDP and a state-of-the-art GP-based policy search method, PDDP offers a superior combination of data-efficiency, learning speed, and applicability.