Causal Projected Gradient Descent: Online Convex Optimization under DAG-Induced Partial Order Constraints.
Year: 2026
Type: preprint
Abstract: We study the constrained optimization problem where the parameter space Theta subset of R^p is equipped with a partial order induced by a directed acyclic graph (DAG). At each step, a convex loss function is revealed, and the parameter update is restricted to a convex cone of directions compatible with the graph structure. We propose Causal Projected Gradient Descent (CPGD) and prove a regret bound of O(sqrt(omega T)), where omega = omega(G) is the width of the partial order, which can be significantly smaller than the ambient dimension p. Additionally, we analyze the problem of estimating the graph G from a sequence of paired observations using a recursive partial correlation test and establish consistency at rate O(1 / sqrt(n)). A connection is established between the use of historical observations in the estimation procedure and Tikhonov-type regularization in the parameter space, providing a theoretical justification for experience replay in continual learning.
Author: Владислав Тишков
Language: English
Field: Decision Sciences
Domain: Social Sciences
Open Access status: green
OpenAlex ID: W7204150015