Game-Agnostic Value Functions through Automatic JSON Feature Extraction

JSON Bag-of-Tokens (JSON-Bag) is a recently proposed method to generically represent game trajectories by tokenizing their JSON descriptions. We introduce JSON-Bag VF, a game-agnostic approach to training value functions for game-playing agents using JSON-Bag prototypes. We show that this approach can be enhanced with Random Forest-based feature selection and a method to select game-stage-specific features. We evaluate JSON-Bag VF with One-step-look-ahead (JSON-Bag OSLA) on six tabletop games over different combinations of prototype-tokenization and feature selections. JSON-Bag OSLA outperforms baseline OSLA agents in most games. Our analysis also shows that feature selection significantly improves JSON-Bag VF and that feature selection is the most important factor in JSON-Bag VF performance, over prototype-tokenization.

Le Critique: Privileged Value Functions for LLM Reinforcement Learning

Reinforcement learning algorithms for Large Language Models (LLMs) are largely distinguished by their variance reduction strategy. Group-relative methods like GRPO reduce gradient variance by sampling multiple rollouts per prompt, but provide only sequence-level credit. Training is also blocked by straggler rollouts, reducing throughput and increasing off-policyness. Learned value functions theoretically address both problems, providing token-level advantages without requiring large groups. However, additional infrastructure engineering challenges combined with the practical success of critic-free methods have made it difficult to justify their inclusion in RL pipelines. We propose two complementary strategies to improve the performance of value function RL: 1) Privileged Value Functions (PVF) which provide an elegant mechanism to inject additional task-relevant token-level signal without biasing the policy objective; 2) TETHER, a baseline that adaptively interpolates between group-relative and value baselines depending on the value function accuracy. Across several reasoning tasks, both strategies consistently improve over the standard value function baseline, and are competitive with or outperform mean-baseline GRPO.

Generalised Bellman recurrence and three dualities in sequential decision-making

What gives the Bellman equation its form? We show that the recursive properties of optimal value functions follow from three conditions: that the dynamics decomposes through sufficient statistics, that the return decomposes recursively, and that the aggregation of uncertainty is compatible with both. When all three conditions hold on a common state, the Bellman equation arises from their mutual consistency; when one fails, tractability can often be recovered by augmenting the state or by deforming return or dynamics. The same conditions are shown to give rise to three dualities: one between probability and return, one between return and aggregation, and one between aggregation and probability. Our framework reveals these dualities as arising from a single construction, unifying methods developed separately across reinforcement learning, control, and decision theory.

A Goal-Set Characterization of Task Composition in the Boolean Task Algebra

The Boolean Task Algebra (BTA) provides a principled framework for zero-shot task composition in reinforcement learning by equipping goal-reaching tasks with Boolean operations. We revisit its structural assumptions and formalize a collapse in the space of optimal extended Q-value functions: in deterministic MDPs, every such function is fully determined by the universal and empty tasks. This makes the logarithmic set of base tasks proposed in the original BTA formulation redundant. Building on this observation, we introduce a goal-set-based composition method that performs logical operations on goal sets and reconstructs composed value functions by selecting slices from the universal and empty value functions. This reduces learning costs for standard BTA and reduces composition time for both BTA and Skill Machines, while preserving policy performance. Experiments across tabular, visual, function-approximation, and continuous-control domains show that learning additional base tasks does not yield better performance. Finally, we study the stochastic setting and provide a counterexample showing that this collapse need not hold, that is, optimal composition may require accounting for exponentially many policies in the number of goals. Code is available at https://github.com/EduardoTerres/bta_paper.

The Value Function Semi-Algebraic Set in Partially Observable Markov Decision Processes

We study the geometry of feasible value functions in infinite-horizon partially observable Markov decision processes (POMDPs) under memoryless stochastic policies. Our main contribution is a characterization of the feasible set of value functions as a semi-algebraic set, defined by explicit polynomial inequalities determined by the transition dynamics, observation kernel, and reward structure of the POMDP. This result extends prior work for fully observable Markov decision processes, where the feasible set is known to be a polytope, to the substantially more intricate partially observable setting. In contrast to the polyhedral structure arising in MDPs, partial observability induces fundamentally nonlinear constraints, leading to a richer and more complex geometric structure. Our geometric characterization provides new insight into the landscape of policy optimization in both MDPs and POMDPs, and reveals qualitative phenomena unique to partial observability, including the emergence of isolated local maximizers of the long-term reward and their dependence on the initial state distribution.