Uncertainty in Artificial Intelligence
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Universal Convexification via Risk-Aversion
Krishnamurthy Dvijotham, Maryam Fazel, Emanuel Todorov
We develop a framework for convexifying a general class of optimization problems. We analyze the suboptimality of the solution to the convexified problem relative to the original nonconvex problem, and prove ad- ditive approximation guarantees under some assumptions. In simple settings, the convexi- fication procedure can be applied directly and standard optimization methods can be used. In the general case we rely on stochastic gra- dient algorithms, whose convergence rate can be bounded using the convexity of the under- lying optimization problem. We then extend the framework to a general class of discrete- time dynamical systems where our convex- ification approach falls under the paradigm of risk-sensitive Markov Decision Processes. We derive the first model-based and model- free policy gradient optimization algorithms with guaranteed convergence to the optimal solution. We also present numerical results in different machine learning applications.
Pages: 162-171
PS Link:
PDF Link: /papers/14/p162-dvijotham.pdf
AUTHOR = "Krishnamurthy Dvijotham and Maryam Fazel and Emanuel Todorov",
TITLE = "Universal Convexification via Risk-Aversion",
BOOKTITLE = "Proceedings of the Thirtieth Conference Annual Conference on Uncertainty in Artificial Intelligence (UAI-14)",
ADDRESS = "Corvallis, Oregon",
YEAR = "2014",
PAGES = "162--171"

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