Long-Horizon RL

Policy gradient methods for Large Language Models optimize a policy $π_θ$ via a surrogate objective computed from samples of a rollout policy $π_{\text{roll}}$. However, modern LLM-RL pipelines suffer from unavoidable implementation divergences -- backend discrepancies, Mixture-of-Experts routing discontinuities, and distributed training staleness -- causing off-policy mismatch ($π_{\text{roll}} \neq π_θ$) and approximation errors between the surrogate and the true objective. We demonstrate that classical trust region bounds on this error scale as $O(T^2)$ with sequence length $T$, rendering them vacuous for long-horizon tasks. To address this, we derive a family of bounds -- both KL-based and TV-based -- including a Pinsker-Marginal bound ($O(T^{3/2})$), a Mixed bound ($O(T)$), and an Adaptive bound that strictly generalizes the Pinsker-Marginal bound via per-position importance-ratio decomposition. Taking the minimum over all bounds yields the tightest known guarantee across all divergence regimes. Crucially, all bounds depend on the maximum token-level divergence $D_{\mathrm{KL}}^{\mathrm{tok,max}}$ (or $D_{\mathrm{TV}}^{\mathrm{tok,max}}$), a sequence-level quantity that cannot be controlled by token-independent methods like PPO clipping. We propose Trust Region Masking (TRM), which masks entire sequences violating the trust region, enabling the first non-vacuous monotonic improvement guarantees for long-horizon LLM-RL.

Reward machines (RMs) inform reinforcement learning agents about the reward structure of the environment, enabling support for non-Markovian tasks and improving sample efficiency. However, learning with RMs is ill-suited for long-horizon problems where subtasks can be completed in any order. In such cases, the amount of information to learn increases exponentially with the number of unordered subtasks. We address this issue by introducing three generalisations of RMs: (1) Numeric RMs allow users to express complex tasks in a compact form. (2) In agenda RMs, states are associated with an agenda that tracks the remaining subtasks to complete. (3) Coupled RMs have coupled states associated with each subtask in the agenda. In addition, we introduce QCoRM, a new task-decomposition Q-learning-based algorithm that leverages coupled RMs and preserves global optimality guarantees in tabular settings. Our experiments across four domains -- featuring both discrete and continuous action and state spaces -- demonstrate that QCoRM scales better than baseline algorithms for long-horizon problems with unordered subtasks.