Non-asymptotic bounds for stochastic optimization with biased noisy gradient oracles

• URL: http://arxiv.org/abs/2002.11440v2
• Date: Sun, 16 May 2021 11:50:36 GMT
• Title: Non-asymptotic bounds for stochastic optimization with biased noisy gradient oracles
• Authors: Nirav Bhavsar and Prashanth L.A
• Abstract summary: We introduce biased gradient oracles to capture a setting where the function measurements have an estimation error. Our proposed oracles are in practical contexts, for instance, risk measure estimation from a batch of independent and identically distributed simulation.
• Score: 8.655294504286635
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We introduce biased gradient oracles to capture a setting where the function measurements have an estimation error that can be controlled through a batch size parameter. Our proposed oracles are appealing in several practical contexts, for instance, risk measure estimation from a batch of independent and identically distributed (i.i.d.) samples, or simulation optimization, where the function measurements are `biased' due to computational constraints. In either case, increasing the batch size reduces the estimation error. We highlight the applicability of our biased gradient oracles 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 for the last iterate of a stochastic gradient descent (SGD) algorithm with a biased gradient oracle.

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