A Structural Threshold in Decision Capacity Governs Collapse in Self-Play Reinforcement Learning

Self-play reinforcement learning trains language models on their own generated tasks, co-evolving a proposer and solver without human labels. Recent systems report strong reasoning gains, but collapse and instability are widely observed and poorly understood. The dominant response treats this as a reward-design problem. We argue instead that self-play stability is governed by two distinct levers: a data-level gate that decides which proposer-generated tasks enter the training pool, and the reward signal that updates the policy on tasks already admitted. Through controlled experiments on a Python output-prediction task and a deterministic-DSL twin task that strips pretraining priors, output ambiguity, and executor noise, we find the two levers are asymmetric. A strict gate is sufficient for stability under every reward variant we test, including a self-consistency reward with no access to ground truth; while no reward variant is sufficient once the gate is removed. This asymmetry exposes a counter-intuitive coupling we call the Grounded Proposer Paradox: a proposer with ground-truth access accelerates collapse faster than an ungrounded one when paired with a self-consistency solver, by concentrating training on clean tasks that form the fastest path to a spurious self-consistent attractor. Replacing the binary gate with a continuous strictness parameter $\varepsilon$ further reveals a two-stage phase transition: training-side metrics decouple at low $\varepsilon$, while validation accuracy holds until $\varepsilon$ is much higher. Data-level gating, not reward calibration, is the binding constraint on self-play stability.

We study adversarial action masking in self-play reinforcement learning: an attacker selectively removes legal actions from a victim's action set. Unlike observation or action perturbations, removal eliminates decision options before the agent acts. Across poker games scaling from 6 to 5,531 information states and two non-poker domains, learned masking causes substantially more damage than random masking and learned perturbation baselines. The attack persists across Q-learning, PPO, NFSP, neural NFSP, and DQN victims; transfers across agents; is amplified by self-play; and shows no recovery under extended masked training. Mechanistically, the adversary targets high-value decision points, captured by reach-weighted contingent action capacity (CAC$_w$) and a value-weighted refinement CAC$_v$. These results identify action availability as a distinct robustness surface in self-play RL.

Self-play with naive gradient ascent cycles in two-player zero-sum games: the last iterate orbits the equilibrium. Modern methods restore last-iterate convergence by regularizing toward a reference policy -- MMD a fixed one (reaching only the regularized equilibrium), R-NaD a periodic snapshot (the engine of DeepNash). We study GARIP, which anchors to the running average, and isolate what the choice of reference controls. Our central result is a mechanism: collapse tracks the peak lag of the reference, and among causal convex averages of a fixed mean lag the running average (flat profile, peak $=$ mean) uniquely minimizes that peak, while a snapshot's sawtooth has peak $= 2\times$ mean (a one-line theorem). Two consequences follow. Convergence: we prove local last-iterate convergence at constant anchor strength -- the anchor scales the base map's rotation by $1-β$, crossing the stability boundary and turning a recurrent base into a contraction (global convergence is conjectured at small $β$; we characterize a large-$β$ consensus failure). Robustness: GARIP matches R-NaD's peak performance -- on matrix games, the Coin Game, and the board games Connect Four/Othello, both moving references are far more robust than fixed-magnet and magnet-free baselines -- but is the better hyperparameter default; we report it both ways: over the full grid collapse rates are statistically indistinguishable, yet at conventional parameterizations a matched-mean-lag setting collapses in 0/40 vs 10/40 seeds (a snapshot matches it only by knowing to shorten $K$). The boundaries: an anticipatory (negative-weight) reference does better still on the stale side, and the advantage appears only where naive self-play cycles (five deep self-play loops). All experiments are pure JAX and reproducible.