Mixed Strategies for Robust Optimization of Unknown Objectives

Pier Giuseppe Sessa, Ilija Bogunovic, Maryam Kamgarpour, Andreas Krause
Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics, PMLR 108:2970-2980, 2020.

Abstract

We consider robust optimization problems, where the goal is to optimize an unknown objective function against the worst-case realization of an uncertain parameter. For this setting, we design a novel sample-efficient algorithm GP-MRO, which sequentially learns about the unknown objective from noisy point evaluations. GP-MRO seeks to discover a robust and randomized mixed strategy, that maximizes the worst-case expected objective value. To achieve this, it combines techniques from online learning with nonparametric confidence bounds from Gaussian processes. Our theoretical results characterize the number of samples required by GP-MRO to discover a robust near-optimal mixed strategy for different GP kernels of interest. We experimentally demonstrate the performance of our algorithm on synthetic datasets and on human-assisted trajectory planning tasks for autonomous vehicles. In our simulations, we show that robust deterministic strategies can be overly conservative, while the mixed strategies found by GP-MRO significantly improve the overall performance.

Cite this Paper


BibTeX
@InProceedings{pmlr-v108-sessa20a, title = {Mixed Strategies for Robust Optimization of Unknown Objectives}, author = {Sessa, Pier Giuseppe and Bogunovic, Ilija and Kamgarpour, Maryam and Krause, Andreas}, booktitle = {Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics}, pages = {2970--2980}, year = {2020}, editor = {Silvia Chiappa and Roberto Calandra}, volume = {108}, series = {Proceedings of Machine Learning Research}, month = {26--28 Aug}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v108/sessa20a/sessa20a.pdf}, url = { http://proceedings.mlr.press/v108/sessa20a.html }, abstract = {We consider robust optimization problems, where the goal is to optimize an unknown objective function against the worst-case realization of an uncertain parameter. For this setting, we design a novel sample-efficient algorithm GP-MRO, which sequentially learns about the unknown objective from noisy point evaluations. GP-MRO seeks to discover a robust and randomized mixed strategy, that maximizes the worst-case expected objective value. To achieve this, it combines techniques from online learning with nonparametric confidence bounds from Gaussian processes. Our theoretical results characterize the number of samples required by GP-MRO to discover a robust near-optimal mixed strategy for different GP kernels of interest. We experimentally demonstrate the performance of our algorithm on synthetic datasets and on human-assisted trajectory planning tasks for autonomous vehicles. In our simulations, we show that robust deterministic strategies can be overly conservative, while the mixed strategies found by GP-MRO significantly improve the overall performance.} }
Endnote
%0 Conference Paper %T Mixed Strategies for Robust Optimization of Unknown Objectives %A Pier Giuseppe Sessa %A Ilija Bogunovic %A Maryam Kamgarpour %A Andreas Krause %B Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2020 %E Silvia Chiappa %E Roberto Calandra %F pmlr-v108-sessa20a %I PMLR %P 2970--2980 %U http://proceedings.mlr.press/v108/sessa20a.html %V 108 %X We consider robust optimization problems, where the goal is to optimize an unknown objective function against the worst-case realization of an uncertain parameter. For this setting, we design a novel sample-efficient algorithm GP-MRO, which sequentially learns about the unknown objective from noisy point evaluations. GP-MRO seeks to discover a robust and randomized mixed strategy, that maximizes the worst-case expected objective value. To achieve this, it combines techniques from online learning with nonparametric confidence bounds from Gaussian processes. Our theoretical results characterize the number of samples required by GP-MRO to discover a robust near-optimal mixed strategy for different GP kernels of interest. We experimentally demonstrate the performance of our algorithm on synthetic datasets and on human-assisted trajectory planning tasks for autonomous vehicles. In our simulations, we show that robust deterministic strategies can be overly conservative, while the mixed strategies found by GP-MRO significantly improve the overall performance.
APA
Sessa, P.G., Bogunovic, I., Kamgarpour, M. & Krause, A.. (2020). Mixed Strategies for Robust Optimization of Unknown Objectives. Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 108:2970-2980 Available from http://proceedings.mlr.press/v108/sessa20a.html .

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