Universal Convexification via Risk-Aversion
Universal Convexification via Risk-Aversion
复制标题
通过风险规避实现万有凸化
DOI：
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
E. Todorov
中科院分区：
文献类型：
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作者：
Krishnamurthy Dvijotham;Maryam Fazel;E. Todorov
We develop a framework for convexifying a fairly general class of optimization problems. Under additional assumptions, we analyze the suboptimality of the solution to the convexified problem relative to the original nonconvex problem and prove additive approximation guarantees. We then develop algorithms based on stochastic gradient methods to solve the resulting optimization problems and show bounds on convergence rates. %We show a simple application of this framework to supervised learning, where one can perform integration explicitly and can use standard (non-stochastic) optimization algorithms with better convergence guarantees. We then extend this framework to apply to a general class of discrete-time dynamical systems. In this context, our convexification approach falls under the well-studied paradigm of risk-sensitive Markov Decision Processes. We derive the first known model-based and model-free policy gradient optimization algorithms with guaranteed convergence to the optimal solution. Finally, we present numerical results validating our formulation in different applications.
