What question did this study set out to answer?

To develop an online convex optimization algorithm that achieves optimal regret and constraint bounds under stochastic constraints without relying on restrictive Slater conditions.

July 8, 2020ACM SIGMETRICS Performance Evaluation Review

Online Primal-Dual Mirror Descent under Stochastic Constraints

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To develop an online convex optimization algorithm that achieves optimal regret and constraint bounds under stochastic constraints without relying on restrictive Slater conditions.
Formulated a primal-dual mirror descent algorithm analyzed under a generalized Lagrange multiplier condition rather than interior-point Slater assumptions.
Derived theoretical bounds for expected regret and constraint violation on general convex sets and probability simplex domains.
Tested algorithmic performance numerically on a data center server provisioning benchmark using real electricity price traces.
Attained O(√T) expected regret alongside O(√T) constraint violation while accommodating general equality constraints under a weaker Lagrange multiplier assumption.
Reduced the dimension dependence of the regret coefficient from polynomial to logarithmic when decision variables are constrained to a probability simplex.
Demonstrated effective cost minimization and constraint satisfaction in data center server provisioning simulations.

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Implication

Algorithmic analysis demonstrates sublinear regret and constraint violation in online convex optimization without Slater conditions, highlighting broader applicability to general equality constraints.

Cite This Study

Wei et al. (2020) studied this question.

synapsesocial.com/papers/6a7457a451ce19f076093466 https://doi.org/10.1145/3410048.3410051

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Online Primal-Dual Mirror Descent under Stochastic Constraints

Key Points

Discussion

Implication

Cite This Study

Online Primal-Dual Mirror Descent under Stochastic Constraints

Key Points

Discussion

Implication

Cite This Study

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