Siqi Du

Heling Zhang, Siqi Du, Roy Dong

Follow-the-regularized-leader (FTRL) algorithms have become popular in the context of games, providing easy-to-implement methods for each agent, as well as theoretical guarantees that the strategies of all agents will converge to some equilibrium concept (provided that all agents follow the appropriate dynamics). However, with these methods, each agent ignores the coupling in the game, and treats their payoff vectors as exogenously given. In this paper, we take the perspective of one agent (the controller) deciding their mixed strategies in a finite game, while one or more other agents update their mixed strategies according to continuous-time FTRL. Viewing the learners' dynamics as a nonlinear control system evolving on the relative interior of a simplex or product of simplices, we ask when the controller can steer the learners to a target state, using only its own mixed strategy and without modifying the game's payoff structure. For the two-player case we provide a necessary and sufficient criterion for controllability based on the existence of a fully mixed neutralizing controller strategy and a rank condition on the projected payoff map. For multi-learner interactions we give two sufficient controllability conditions, one based on uniform neutralization and one based on a periodic-drift hypothesis together with a Lie-algebra rank condition. We illustrate these results on canonical examples such as Rock-Paper-Scissors and a construction related to Brockett's integrator.

Jung-Hoon Cho, Heling Zhang, Siqi Du et al.

Policies must operate across diverse conditions, yet a single policy is often conservative while fully adaptive schemes can be complex. We study zero-shot generalization in contextual dynamical systems and introduce a performance-centric, directional task dissimilarity--the signed divergence--that upper bounds the generalization gap from a source context to a target context. The signed divergence induces $\varepsilon$-tolerance sets that certify when a source policy class generalizes, and it yields a concrete notion of task-space complexity: the minimum number of source contexts needed so that every target context incurs at most $\varepsilon$ generalization gap. Under a mild local smoothness assumption on performance, the induced tolerance sets admit certified inner/outer balls and instance-dependent volume bounds on task-space complexity. In the finite-oracle setting, source selection reduces to set cover; a greedy strategy inherits the standard $H(n)$ approximation guarantee. Using a Mass-Spring-Damper system with linear-quadratic regulator (LQR) controllers and a nonlinear CartPole system with deep reinforcement learning controllers, we show that greedy selection achieves the same $\varepsilon$-coverage with fewer policies than uniform or random baselines. Our approach delivers a performance-based task similarity measure and practical certificates for building generalizable control with simple policies.