Online Convex Optimization With Binary Constraints
We consider online optimization with binary decision variables and convex loss functions. We design a new algorithm, binary online gradient descent ( bOGD ) and bound its expected dynamic regret. We provide a regret bound that holds for any time horizon and a specialized bound for finite time horizo...
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| Veröffentlicht in: | IEEE transactions on automatic control 2021-12, Vol.66 (12), p.6164-6170 |
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| container_title | IEEE transactions on automatic control |
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| creator | Lesage-Landry, Antoine Taylor, Joshua A. Callaway, Duncan S. |
| description | We consider online optimization with binary decision variables and convex loss functions. We design a new algorithm, binary online gradient descent ( bOGD ) and bound its expected dynamic regret. We provide a regret bound that holds for any time horizon and a specialized bound for finite time horizons. First, we present the regret as the sum of the relaxed, continuous round optimum tracking error, and the rounding error of our update in which the former asymptomatically decreases with time under certain conditions. Then, we derive a finite-time bound that is sublinear in time and linear in the cumulative variation of the relaxed, continuous round optima. We apply bOGD to demand response with thermostatically controlled loads, in which binary constraints model discrete on/off settings. We also model uncertainty and varying load availability, which depend on temperature deadbands, lockout of cooling units and manual overrides. We test the performance of bOGD in several simulations based on demand response. The simulations corroborate that the use of randomization in bOGD does not significantly degrade performance while making the problem more tractable. |
| doi_str_mv | 10.1109/TAC.2021.3061625 |
| format | Article |
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We design a new algorithm, binary online gradient descent ( bOGD ) and bound its expected dynamic regret. We provide a regret bound that holds for any time horizon and a specialized bound for finite time horizons. First, we present the regret as the sum of the relaxed, continuous round optimum tracking error, and the rounding error of our update in which the former asymptomatically decreases with time under certain conditions. Then, we derive a finite-time bound that is sublinear in time and linear in the cumulative variation of the relaxed, continuous round optima. We apply bOGD to demand response with thermostatically controlled loads, in which binary constraints model discrete on/off settings. We also model uncertainty and varying load availability, which depend on temperature deadbands, lockout of cooling units and manual overrides. We test the performance of bOGD in several simulations based on demand response. 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We design a new algorithm, binary online gradient descent ( bOGD ) and bound its expected dynamic regret. We provide a regret bound that holds for any time horizon and a specialized bound for finite time horizons. First, we present the regret as the sum of the relaxed, continuous round optimum tracking error, and the rounding error of our update in which the former asymptomatically decreases with time under certain conditions. Then, we derive a finite-time bound that is sublinear in time and linear in the cumulative variation of the relaxed, continuous round optima. We apply bOGD to demand response with thermostatically controlled loads, in which binary constraints model discrete on/off settings. We also model uncertainty and varying load availability, which depend on temperature deadbands, lockout of cooling units and manual overrides. We test the performance of bOGD in several simulations based on demand response. The simulations corroborate that the use of randomization in bOGD does not significantly degrade performance while making the problem more tractable.</description><subject>Algorithms</subject><subject>Binary decision</subject><subject>Computational geometry</subject><subject>Constraint modelling</subject><subject>Convex functions</subject><subject>Convexity</subject><subject>Decision theory</subject><subject>Demand response</subject><subject>dynamic regret</subject><subject>online convex optimization</subject><subject>Optimization</subject><subject>Performance degradation</subject><subject>Rounding</subject><subject>thermostatically controlled loads</subject><subject>Tracking errors</subject><issn>0018-9286</issn><issn>1558-2523</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><sourceid>RIE</sourceid><recordid>eNo9kE1LAzEQhoMouFbvgpcFz1szk4_dHOtiVSj0UvEYsrtZTGmzNUlF_fVuafE0DPO8M8NDyC3QKQBVD6tZPUWKMGVUgkRxRjIQoipQIDsnGaVQFQoreUmuYlyPreQcMoJLv3He5vXgv-x3vtwlt3W_JrnB5-8ufeSPzpvwc5jHFIzzKV6Ti95sor051Ql5mz-t6pdisXx-rWeLomWMpaJqeQ9MlEZA26NUreTQ0aqnDeuahjcoGAgsO64Eb5jsOiu7RqFEA8qCadmE3B_37sLwubcx6fWwD348qVFSUQJSiiNFj1QbhhiD7fUuuO34sgaqD2b0aEYfzOiTmTFyd4w4a-0_rpgElBX7A07PXaE</recordid><startdate>20211201</startdate><enddate>20211201</enddate><creator>Lesage-Landry, Antoine</creator><creator>Taylor, Joshua A.</creator><creator>Callaway, Duncan S.</creator><general>IEEE</general><general>The Institute of Electrical and Electronics Engineers, Inc. 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| source | IEEE Electronic Library (IEL) |
| subjects | Algorithms Binary decision Computational geometry Constraint modelling Convex functions Convexity Decision theory Demand response dynamic regret online convex optimization Optimization Performance degradation Rounding thermostatically controlled loads Tracking errors |
| title | Online Convex Optimization With Binary Constraints |
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