Partially Informed Stochastic Optimization via Zeroth-Order Residual Tracking
PISO tracks unknown gradient residuals with zeroth-order probes for partially observed stochastic optimization.
PISO addresses optimization where only part of the gradient is observed and the rest must be inferred from function evaluations, including performative prediction, performative reinforcement learning, and black-box bilevel problems. It centres zeroth-order probes on a running residual estimate so variance tracks the estimation error. For smooth nonconvex objectives, stated complexities are O(d²ε⁻⁶) under Lipschitz gradients and O(d²ε⁻⁵) with a Lipschitz Hessian, using one probe, two function samples, and one known-component sample per update. Variants improve on tested baselines with comparable oracle access in three of five settings.
- Combines a known gradient component with a tracked residual estimate
- Probe variance depends on tracking error rather than residual size
- Reports O(d²ε⁻⁶) and O(d²ε⁻⁵) function-evaluation complexities
- Beats comparable-oracle baselines in three of five tested settings
From the original article
1 min read at arxiv.orgMany optimization problems provide direct access to only part of the gradient, while the remaining component must be inferred from function evaluations. This structure arises in performative prediction, performative reinforcement learning, and bilevel optimization with a black-box lower level.
By El Mahdi Chayti · arxiv.org
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