paper

Online convex optimization for cumulative constraints

arXiv:1802.06472

Abstract

We propose the algorithms for online convex optimization which lead to cumulative squared constraint violations of the form , where . Previous literature has focused on long-term constraints of the form . There, strictly feasible solutions can cancel out the effects of violated constraints. In contrast, the new form heavily penalizes large constraint violations and cancellation effects cannot occur. Furthermore, useful bounds on the single step constraint violation are derived. For convex objectives, our regret bounds generalize existing bounds, and for strongly convex objectives we give improved regret bounds. In numerical experiments, we show that our algorithm closely follows the constraint boundary leading to low cumulative violation.

arXiv commentThe NeurIPS version of the stepsize setup for strongly convex case is not correct. Please see this arxiv setup(e.g.,move the H1 to the denominator)

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