Non-asymptotic bounds for stochastic optimization with a biased noisy gradient oracle
We introduce an optimization oracle to capture a setting where the function measurements
have an estimation error that can be controlled through a batch size parameter. Our
proposed `biased gradient oracle' is appealing in practical contexts, where either the
objective has to be estimated from Markovian samples, or the estimation scheme is 'biased'
due to computational constraints. In either case, increasing the batch size reduces the
estimation error. We highlight the applicability of our biased gradient oracle in a
risk-sensitive reinforcement learning setting. In the stochastic non-convex optimization
context, we analyze a variant of the randomized stochastic gradient (RSG) algorithm with
a biased gradient oracle. We quantify the convergence rate of this algorithm by deriving
non-asymptotic bounds on its performance. Next, in the stochastic convex optimization
setting, we derive non-asymptotic bounds that hold in expectation for the last iterate of a
stochastic gradient descent (SGD) algorithm.
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- kanpur, Uttar Pradesh
- India 208016
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Prashanth L.A
Non-asymptotic bounds for stochastic optimization with a biased noisy gradient oracle
Biography:
Prashanth L.A. is an Assistant Professor in the Department of Computer Science and Engineering at Indian Institute of Technology Madras. Prior to this, he was a postdoctoral researcher at the Institute for Systems Research, University of Maryland - College Park from 2015 to 2017 and at INRIA Lille - Team SequeL from 2012 to 2014. From 2002 to 2009, he was with Texas Instruments (India) Pvt Ltd, Bangalore, India.
He received his Masters and Ph.D degrees in Computer Science and Automation from Indian Institute of Science, in 2008 and 2013, respectively. He was awarded the third prize for his Ph.D. dissertation, by the IEEE Intelligent Transportation Systems Society (ITSS). He is the coauthor of a book entitled 'Stochastic Recursive Algorithms for Optimization: Simultaneous Perturbation Methods', published by Springer in 2013. His research interests are in reinforcement learning, simulation optimization and multi-armed bandits, with applications in transportation systems, wireless networks and recommendation systems.
Address:India