Parametric Open Source Games

Open-source game theory studies agents whose behavior may depend on one another's decision procedures, but most existing models use discrete or symbolic programs. We introduce parametric open-source games, a continuous analogue of program equilibria in which players choose parameter vectors and semantics maps convert the full parameter profile into mixed actions in an underlying finite game. We establish equilibrium existence results, derive an exact coupling threshold at which selfish gradient ascent in symmetric $2\times2$ games switches from defection toward cooperation, and give a one-dimensional boundary test for parametric program Nash equilibria. We further extend the framework to a neural semantics class whose first-order cooperation condition is governed by the ratio of cross-player to self-player sensitivity. Across canonical games, the framework shows how access to internal parameterizations can qualitatively reshape learning dynamics and equilibrium structure, and how sufficiently strong open-source coupling can steer selfish optimization toward cooperative outcomes.

Trace-Mediated Peak Bias: Bridging Temporal Credit Assignment and Cognitive Heuristics in Deep Reinforcement Learning

Temporal credit assignment is central to both biological and artificial intelligence, yet its interaction with non-linear function approximation is poorly understood. We identify a systematic failure mode in deep reinforcement learning (RL) termed Trace-Mediated Peak Bias (TMPB). At intermediate eligibility trace depths, agents irrationally prefer trajectories with high-magnitude reward ``peaks'' over alternatives with higher cumulative returns. This provides a mechanistic account of the Peak-End Rule: a human memory bias where experiences are judged by their most intense moments rather than integrated utility. We show that TMPB emerges because traces amplify distal Temporal Difference errors into ``gradient shocks'' that fixed-step-size Stochastic Gradient Descent cannot normalize, leading to global overestimation. Conversely, adaptive optimizers mitigate this pathology via second-moment normalization. Our results suggest that human-like saliency distortions may emerge naturally from the mathematical constraints of credit assignment in distributed systems, and that adaptive optimization is a theoretical necessity for rational value estimation.

Learning in Low-Dimensional Subspaces: Orthogonal Bottlenecks for Reinforcement Learning

Deep reinforcement learning (RL) agents commonly rely on high-dimensional neural representations, despite growing evidence that task-relevant value and policy structure may be intrinsically low-dimensional. In this work, we present a simple yet effective representation-level prior that inserts a fixed orthonormal projection to constrain encoder features to a low-dimensional subspace, requiring no auxiliary objectives, pretraining, or changes to the underlying RL algorithm. Under a linear realizability assumption, we prove that when the bottleneck dimension exceeds the intrinsic rank of the optimal value function in feature space, the bottleneck preserves expressivity and leaves the induced gradient dynamics unchanged up to an equivalent low-dimensional parameterization. Empirically, we find that across both single and multi-task benchmarks, baseline performance is either matched or improved once the bottleneck dimension exceeds a small task-dependent threshold; in many cases, value representations can be compressed to extremely low dimensions without loss, and the minimal sufficient dimension depends far more on environment complexity than encoder width. In addition, we analyze representation geometry and find that orthogonal bottlenecks stabilize feature norms and are associated with higher effective rank. Together, these results support a representation-space interpretation of the manifold hypothesis in reinforcement learning and position orthogonal bottlenecks as a lightweight, architecture-agnostic mechanism for shaping RL representations.

On The Presence of Double-Descent in Deep Reinforcement Learning

The double descent (DD) paradox, where over-parameterized models see generalization improve past the interpolation point, remains largely unexplored in the non-stationary domain of Deep Reinforcement Learning (DRL). We present preliminary evidence that DD exists in model-free DRL, investigating it systematically across varying model capacity using the Actor-Critic framework. We rely on an information-theoretic metric, Policy Entropy, to measure policy uncertainty throughout training. Preliminary results show a clear epoch-wise DD curve; the policy's entrance into the second descent region correlates with a sustained, significant reduction in Policy Entropy. This entropic decay suggests that over-parameterization acts as an implicit regularizer, guiding the policy towards robust, flatter minima in the loss landscape. These findings establish DD as a factor in DRL and provide an information-based mechanism for designing agents that are more general, transferable, and robust.

Sparsity-Driven Plasticity in Multi-Task Reinforcement Learning

Plasticity loss, a diminishing capacity to adapt as training progresses, is a critical challenge in deep reinforcement learning. We examine this issue in multi-task reinforcement learning (MTRL), where higher representational flexibility is crucial for managing diverse and potentially conflicting task demands. We systematically explore how sparsification methods, particularly Gradual Magnitude Pruning (GMP) and Sparse Evolutionary Training (SET), enhance plasticity and consequently improve performance in MTRL agents. We evaluate these approaches across distinct MTRL architectures (shared backbone, Mixture of Experts, Mixture of Orthogonal Experts) on standardized MTRL benchmarks, comparing against dense baselines, and a comprehensive range of alternative plasticity-inducing or regularization methods. Our results demonstrate that both GMP and SET effectively mitigate key indicators of plasticity degradation, such as neuron dormancy and representational collapse. These plasticity improvements often correlate with enhanced multi-task performance, with sparse agents frequently outperforming dense counterparts and achieving competitive results against explicit plasticity interventions. Our findings offer insights into the interplay between plasticity, network sparsity, and MTRL designs, highlighting dynamic sparsification as a robust but context-sensitive tool for developing more adaptable MTRL systems.