Proximity Operators of Discrete Information Divergences

While phi-divergences have been extensively studied in convex analysis, their use in optimization problems often remains challenging. In this regard, one of the main shortcomings of existing methods is that the minimization of phi-divergences is usually performed with respect to one of their arguments, possibly within alternating optimization techniques. In this paper, we overcome this limitation by deriving new closed-form expressions for the proximity operator of such two-variable functions. This makes it possible to employ standard proximal methods for efficiently solving a wide range of convex optimization problems involving phi-divergences. In addition, we show that these proximity operators are useful to compute the epigraphical projection of several functions. The proposed proximal tools are numerically validated in the context of optimal query execution within database management systems, where the problem of selectivity estimation plays a central role. Experiments are carried out on small to large scale scenarios.


Published in:
Ieee Transactions On Information Theory, 64, 2, 1092-1104
Year:
Feb 01 2018
Publisher:
Piscataway, IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
ISSN:
0018-9448
1557-9654
Keywords:
Laboratories:




 Record created 2018-12-13, last modified 2019-06-19


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