Constrained Reinforcement Learning Using Successor Representations

Real-world Reinforcement Learning depends on the ability to formulate safety constraints into a policy. A common way to model such constraints is to introduce an additional cost signal in the Markov Decision Process, which notifies the agent of unwanted behavior independently of the reward signal. Unfortunately, current methods are hard to adapt to changes in the cost function introduced by, e.g., domain shift or obstacles moving over time. The lack of adaptability means that policies are too unflexible to deal with complex real-world conditions. We propose the Safe Deep Successor Representation (SafeDSR), a novel method that allows quick retraining of policies towards new cost structures. SafeDSR extends the Deep Successor Representation (Kulkarni et al., 2016) to Constrained Reinforcement Learning by introducing a single learnable weight matrix to decouple the learned value function across dynamics, rewards, and costs. This matrix can be updated in a supervised manner instead of having to adapt the whole network if the cost structure of the environment changes. We demonstrate this ability in a freely configurable two-dimensional navigation environment and show that our method is competitive on a simple navigation task while being considerably more flexible

Bias-Controlled Primal-Dual Natural Actor-Critic: Optimal Rates for Constrained Multi-Objective Average-Reward RL

Many reinforcement learning (RL) problems in the infinite-horizon average-reward setting require optimizing multiple conflicting objectives while satisfying multiple safety constraints. A common approach is concave scalarization, where the agent maximizes a utility $ f(J^π_{r_1}, \ldots, J^π_{r_M}) $ subject to a scalarized constraint $ g(J^π_{c_1}, \ldots, J^π_{c_N}) \ge 0 $, where $J^π_{r_m}$ and $J^π_{c_n}$ denote the average-reward and cost under policy $π$. However, the nonlinearity of $f$ and $g$ introduces bias in policy-gradient and actor-critic methods, since gradients must be evaluated using noisy estimates of $J^π,$ and $ \mathbb{E}[\partial f(J^π)] \neq \partial f(\mathbb{E}[J^π]),$ and this bias propagates through both primal and dual updates. We propose an MLMC-based primal-dual Natural Actor-Critic algorithm for average-reward MDPs that controls bias in scalarized objectives, constraint evaluation, and actor-critic estimation without requiring mixing-time knowledge. We show that the algorithm achieves optimal global convergence and constraint-violation rates of $ \tilde{O}(1/\sqrt{T}) $. To our knowledge, this is the first result establishing optimal convergence for concave scalarized multi-objective RL in the average-reward setting, both with and without constraints, and the first to do so without mixing-time information even in the absence of scalarization.

Utility-Constrained Policy Optimization

Constrained MDPs (CMDPs) are a widely adopted framework for incorporating safety into RL agents; however, the framework does not support risk-sensitive constraints. This can be problematic: For example, CMDPs allow for optimal solutions that, in order to satisfy the risk-neutral constraints, mix infrequent catastrophic behaviors and frequent, overly conservative ones. Moreover, prior empirical results suggest that enforcing stricter, risk-sensitive constraints can improve performance even under risk-neutral evaluation. The natural framework to incorporate risk-sensitive constraints is utility-constrained MDPs (UCMDPs), but no practical solutions for this problem existed. In this work, we introduce a simple yet powerful methodology for UCMDPs and constrained RL. Besides allowing for risk-sensitive constraints, our framework does not require us to fix constraint limits in advance of training the agent, provided that a sensible range is known. This increases policy flexibility and, in practice, allows for adjustments to these limits at no extra training cost. Besides benefiting from the generality of the framework, our agent shows strong performance in practice, consistently matching or outperforming existing baselines in several Safety Gymnasium benchmark tasks.

Coordination Graphs for Constrained Multi-Agent Reinforcement Learning

Constrained Multi-agent reinforcement learning (CMARL) faces two intertwined challenges: the joint action space grows exponentially with the number of agents, and additional requirements couple agents in ways that reward structure alone does not capture. We introduce Coordination Graphs for Constrained Multi-Agent Reinforcement Learning (CG-CMARL), a framework that addresses both challenges by combining coordination graphs with Lagrangian duality. The system decomposes the joint problem into pairwise regions, each served by a set of shared Q-functions, one for the primary objective and one for each of the constraints, so that the number of learned models is independent of the number of agents. At execution time, Max-Sum message passing coordinates actions across the factor graph, while a Lagrangian multiplier controls the objective--constraint tradeoff, allowing a single trained model to trace a Pareto front without retraining. We provide convergence guarantees under mild conditions, together with a compositional error bound that decomposes into separate interpretable sources, each traceable to a specific design choice and independently controllable. Experiments on cooperative navigation tasks (where teams of up to 10 agents must coordinate to reach target positions while satisfying pairwise constraints) show that our method produces Pareto fronts dominating established baselines trained at fixed reward-shaping ratios, while scaling to team sizes where centralized approaches become intractable.