For convex losses in nested evolving feasible sets, a lazy algorithm balances O(T^{1-β}) regret with O(T^β) movement for any β; for strongly convex or sharp losses, Frugal achieves zero regret with O(log T) movement, shown optimal by matching lower bound.
Smoothed online convex optimization in high dimensions via online balanced descent
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Convex Optimization with Nested Evolving Feasible Sets
For convex losses in nested evolving feasible sets, a lazy algorithm balances O(T^{1-β}) regret with O(T^β) movement for any β; for strongly convex or sharp losses, Frugal achieves zero regret with O(log T) movement, shown optimal by matching lower bound.