David Sewell | Searcharxiv

arXiv2026

Neural Operators for Multi-Task Control and Adaptation

Neural operator methods have emerged as powerful tools for learning mappings between infinite-dimensional function spaces, yet their potential in optimal control remains largely unexplored. We focus on multi-task control problems, whose solution is a mapping from task description (e.g., cost or dynamics functions) to optimal control law (e.g., feedback policy). We approximate these solution operators using a permutation-invariant neural operator architecture. Across a range of parametric optimal control environments and a locomotion benchmark, a single operator trained via behavioral cloning accurately approximates the solution operator and generalizes to unseen tasks, out-of-distribution settings, and varying amounts of task observations. We further show that the branch-trunk structure of our neural operator architecture enables efficient and flexible adaptation to new tasks. We develop structured adaptation strategies ranging from lightweight updates to full-network fine-tuning, achieving strong performance across different data and compute settings. Finally, we introduce meta-trained operator variants that optimize the initialization for few-shot adaptation. These methods enable rapid task adaptation with limited data and consistently outperform a popular meta-learning baseline. Together, our results demonstrate that neural operators provide a unified and efficient framework for multi-task control and adaptation.

cs.LG↗

arXiv2025

Disc Game Dynamics: A Latent Space Perspective on Selection and Learning in Games

Evolutionary game theory studies populations that change in response to an underlying game. Often, the functional form relating outcome to player attributes or strategy is complex, preventing mathematical progress. In this work, we axiomatically derive a latent space representation for pairwise, symmetric, zero-sum games by seeking a coordinate space in which the optimal training direction for an agent responding to an opponent depends only on their opponent's coordinates. The associated embedding represents the original game as a linear combination of copies of a simple game, the disc game, in a new coordinate space. In this article, we show that disc-game embedding is useful for studying learning dynamics. We demonstrate that a series of classical evolutionary processes simplify to constrained oscillator equations in the latent space. In particular, the continuous replicator equation reduces to a Hamiltonian system of coupled oscillators that exhibit Poincar\'e recurrence. This reduction allows exact, finite-dimensional closure when the underlying game is finite-rank, and optimal approximation otherwise. It also establishes an exact equivalence between the continuous replicator equation and adaptive dynamics in the transformed coordinates. By identifying a minimal rank representation, the disc game embedding offers numerical methods that could decouple the cost of simulation from the number of attributes used to define agents. These results generalize to metapopulation models that mix inhomogeneously, and to any time-differentiable dynamic where the rate of growth of a type, relative to its expected payout, is a nonnegative function of its frequency. We recommend disc-game embedding as an organizing paradigm for learning and selection in response to symmetric two-player zero-sum games.

cs.GT↗