Critic-Free Policy Iteration for Continuous-Time Zero-Sum Games: A Policy-Space Riccati Approach

Abstract

This paper develops a critic-free policy iteration (PI) method for continuous-time linear zero-sum games. The central idea is to characterize the saddle-point policies directly in the joint policy space, rather than treating the quadratic value matrix as an iterative variable. A policy game Riccati equation (PGRE) is introduced whose unknowns are policy gains only. Its solutions are shown to be in one-to-one correspondence with the symmetric solutions of the game algebraic Riccati equation. Based on a stabilizing anchor, PI is performed directly in the actor space. The actor-space Jacobian is nonsingular at every stabilizing policy, and the resulting policy sequence coincides with that of simultaneous PI. For unknown dynamics, a data-driven algorithm uses a single batch of data and nullspace projection of endpoint increments to eliminate the value matrix, yielding an actor-only regression. A necessary and sufficient rank condition for unique policy recovery is established and shown to be iteration-invariant, demonstrating that critic identifiability is unnecessary. A power systems frequency-regulation example verifies convergence and policy recovery, while scalability tests demonstrate substantial reductions in computational and memory requirements.