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Online convex optimization for cumulative constraints
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use clipped constraints and a violation-dependent multiplier update instead of ordinary long-term constraint handling | Online convex optimization with convex losses · Online convex optimization, convex losses | cumulative squared clipped constraint violation: O(T^{3/4}) -> O(\sqrt{T}) | Helped |
| Use time-varying stepsizes for strongly convex losses | Clipped-OGD · Online convex optimization, strongly convex losses | regret: O(\log(T)) | Helped |
| Use time-varying stepsizes for strongly convex losses | Clipped-OGD · Online convex optimization, strongly convex losses | cumulative clipped constraint violation: O(\sqrt{\log(T) T}) | Helped |
| Use the proposed update to control each step's clipped violation | Clipped-OGD · One differentiable constraint | single-step clipped constraint violation: O(\frac{1}{T^{1/6}}) | Helped |
| Replace the ordinary constraint with its clipped positive part | OGD · Toy experiment | trajectory adherence to the constraint boundary | Helped |
| Use the strongly convex update rather than the convex update | Doubly-stochastic matrix approximation · Doubly-stochastic matrices | objective regret | Helped |
| Use the strongly convex update rather than the convex update | Doubly-stochastic matrix approximation · Doubly-stochastic matrices | clipped constraint violation | Helped |
| Use clipped-constraint handling rather than OGD or A-OGD | Economic dispatch · Economic dispatch | single-step constraint violation | Helped |
| Use clipped-constraint handling rather than A-OGD | Toy experiment · Toy experiment | objective regret | Mixed |
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