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- W3092013327 abstract "In this paper, we consider the maximizing of the probability $${mathbb {P}}left{ , zeta , mid , zeta , in , {mathbf {K}}({mathbf {x}}) , right} $$ over a closed and convex set $${mathcal {X}}$$ , a special case of the chance-constrained optimization problem. Suppose $${mathbf {K}}({mathbf {x}}) , triangleq , left{ , zeta , in , {mathcal {K}}, mid , c({mathbf {x}},zeta ) , ge , 0 right} $$ , and $$zeta $$ is uniformly distributed on a convex and compact set $${mathcal {K}}$$ and $$c({mathbf {x}},zeta )$$ is defined as either $$c({mathbf {x}},zeta ), triangleq , 1-left| zeta ^T{mathbf {x}}right| ^m$$ where $$mge 0$$ (Setting A) or $$c({mathbf {x}},zeta ) , triangleq , T{mathbf {x}}, - , zeta $$ (Setting B). We show that in either setting, by leveraging recent findings in the context of non-Gaussian integrals of positively homogenous functions, $${mathbb {P}}left{ ,zeta , mid , zeta , in , {mathbf {K}}({mathbf {x}}) , right} $$ can be expressed as the expectation of a suitably defined continuous function $$F(bullet ,xi )$$ with respect to an appropriately defined Gaussian density (or its variant), i.e. $${mathbb {E}}_{{{tilde{p}}}} left[ , F({mathbf {x}},xi ), right] $$ . Aided by a recent observation in convex analysis, we then develop a convex representation of the original problem requiring the minimization of $$gleft( {mathbb {E}}left[ , F(bullet ,xi ), right] right) $$ over $${mathcal {X}}$$ , where g is an appropriately defined smooth convex function. Traditional stochastic approximation schemes cannot contend with the minimization of $$gleft( {mathbb {E}}left[ F(bullet ,xi )right] right) $$ over $$mathcal X$$ , since conditionally unbiased sampled gradients are unavailable. We then develop a regularized variance-reduced stochastic approximation (r-VRSA) scheme that obviates the need for such unbiasedness by combining iterative regularization with variance-reduction. Notably, (r-VRSA) is characterized by almost-sure convergence guarantees, a convergence rate of $$mathcal {O}(1/k^{1/2-a})$$ in expected sub-optimality where $$a > 0$$ , and a sample complexity of $$mathcal {O}(1/epsilon ^{6+delta })$$ where $$delta > 0$$ . To the best of our knowledge, this may be the first such scheme for probability maximization problems with convergence and rate guarantees. Preliminary numerics on a portfolio selection problem (Setting A) and a set-covering problem (Setting B) suggest that the scheme competes well with naive mini-batch SA schemes as well as integer programming approximation methods." @default.
- W3092013327 created "2020-10-15" @default.
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- W3092013327 date "2022-09-08" @default.
- W3092013327 modified "2023-09-26" @default.
- W3092013327 title "Probability maximization via Minkowski functionals: convex representations and tractable resolution" @default.
- W3092013327 cites W1494085563 @default.
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- W3092013327 cites W1987083649 @default.
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- W3092013327 cites W1994616650 @default.
- W3092013327 cites W2000587848 @default.
- W3092013327 cites W2008685729 @default.
- W3092013327 cites W2014838276 @default.
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- W3092013327 cites W2049606892 @default.
- W3092013327 cites W2053391173 @default.
- W3092013327 cites W2061570747 @default.
- W3092013327 cites W2066778083 @default.
- W3092013327 cites W2068800669 @default.
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- W3092013327 cites W2083350518 @default.
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- W3092013327 cites W2093304942 @default.
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- W3092013327 cites W2099506495 @default.
- W3092013327 cites W2102379475 @default.
- W3092013327 cites W2118382239 @default.
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- W3092013327 cites W2139869783 @default.
- W3092013327 cites W2143514150 @default.
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- W3092013327 cites W2293574808 @default.
- W3092013327 cites W2405594452 @default.
- W3092013327 cites W2438521089 @default.
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- W3092013327 cites W2569380384 @default.
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- W3092013327 cites W2984763623 @default.
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- W3092013327 doi "https://doi.org/10.1007/s10107-022-01859-8" @default.
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