311. Nonsmooth Implicit Differentiation: Deterministic and Stochastic Convergence Rates
Invited abstract in session TB-7: Nonsmooth Bilevel Optimization, stream Bilevel and multilevel optimization.
Tuesday, 10:30-12:30Room: B100/5015
Authors (first author is the speaker)
| 1. | Saverio Salzo
|
| DIAG, Sapienza Università di Roma |
Abstract
I will address the problem of efficiently computing a generalized derivative of the fixed-point of a parametric nondifferentiable contraction map. This problem has wide applications in machine learning, including hyperparameter optimization, meta-learning and data poisoning attacks. Two popular approaches are analyzed: iterative differentiation (ITD) and approximate implicit differentiation (AID). A key challenge behind the nonsmooth setting is that the chain rule does not hold anymore. Building upon the recent work by Bolte et al. (2022), who proved linear convergence of nondifferentiable ITD, I will show an improved linear rate for ITD and a slightly better rate for AID, both in the deterministic case. I will also introduce NSID, a new stochastic method to compute the implicit derivative when the fixed point is defined as the composition of an outer map and an inner map which is accessible only through a stochastic unbiased estimator. Rates for such stochastic method rates will be presented.
Keywords
- Multi-level optimization
- Non-smooth optimization
- Stochastic optimization
Status: accepted
Back to the list of papers