Stochastic gradient ascent with averaging learns Lagrangian multipliers for MILP at the minimax rate Θ(s/√N) and faster Θ(s/N) for warm-start, closing the gap between upper and lower bounds.
arXiv preprint arXiv:2011.07177 , year=
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Stochastic integer optimization has sample complexity that matches, undercuts, or exceeds the continuous case based on objective structure, with new tight bounds for nonconvex continuous problems.
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Provably Data-driven Lagrangian Relaxation for Mixed Integer Linear Programming
Stochastic gradient ascent with averaging learns Lagrangian multipliers for MILP at the minimax rate Θ(s/√N) and faster Θ(s/N) for warm-start, closing the gap between upper and lower bounds.
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Sample Complexity of Stochastic Optimization with Integer Variables
Stochastic integer optimization has sample complexity that matches, undercuts, or exceeds the continuous case based on objective structure, with new tight bounds for nonconvex continuous problems.