Stochastic Decision Horizons for Constrained Reinforcement Learning

Abstract

We propose stochastic decision horizons (SDH), a theoretically grounded framework for solving constrained RL problems with every-step constraint satisfaction, a desirable property in many real-world applications. In SDH, a constraint violation yields an effective shortening of horizon via a state-action continuation probability. Using Control as Inference, we develop the first off-policy and regularized algorithms for RL with instantaneous constraints. We identify two principled semantics for what counts as a decision after a violation. Absorbing-state semantics end the decision process, so only surviving decisions pay entropy cost, yielding max-entropy AS-SAC. Virtual-termination keeps the decision process alive while stopping reward credit, yielding KL-regularized VT-MPO. To connect SDH with CMDPs, we track how violations accumulate along trajectories (their violation-depth profile). SDH effectively weights each trajectory by the exponential of its total violation; this matches an additive CMDP budget exactly when violations occur at a single characteristic scale, and we pinpoint where it cannot: when rare, deep violations mix with frequent, shallow ones. Experiments validate the theory. On the 90-muscle H2190 humanoid (Hyfydy), VT-MPO matches state-of-the-art gait realism with $4\times$ fewer environment steps and substantially more stable training. On Safety Gymnasium, violation-depth profiles correctly identify the regimes in which SDH delivers strong reward-violation trade-offs. Experiments validate the theory. On the 90-muscle H2190 humanoid (Hyfydy), VT-MPO matches state-of-the-art gait realism with 4x fewer environment steps and substantially more stable training. On Safety Gymnasium, violation-depth profiles correctly identify the regimes in which SDH delivers strong reward-violation trade-offs.