arXiv subjects

Anthony Palmieri

Publications and source records attributed to Anthony Palmieri.

3 recordsLinked to original sources

arXiv2026

Extrapolation-based Direct Search for Nonsmooth Stochastic Zeroth-Order Optimization

We propose and analyze a stochastic direct-search method for unconstrained zeroth-order minimization of locally Lipschitz, possibly nonsmooth, objectives. The method combines random polling directions with a stochastic extrapolating line search based on a sufficient-decrease test of order $p$. Under conditional accuracy assumptions on the stochastic estimates, we prove almost-sure convergence to Clarke stationary points. We further establish an expected iteration complexity bound. Specifically, using a supermartingale stopping-time argument, we prove that $\mathcal O\left( \max\left\{ r^{-p}, \varepsilon^{-p/(p-1)} \right\} \right) $ iterations are sufficient in expectation to reach an $(r,\varepsilon)$-Goldstein stationary point. Moreover, we derive a corresponding expected tested-point complexity bound of order $\mathcal O\bigl(\varepsilon^{1-n} \max\{r^{-p},\varepsilon^{-p/(p-1)}\}\bigr)$. To the best of our knowledge, this is the first convergence and expected-complexity analysis for an extrapolation-based direct-search method in a nonsmooth stochastic setting. Numerical experiments on a DFO benchmark suite highlight competitive performance against well-established stochastic direct-search methods.

math.OC↗

arXiv2026

Iteration Complexity of Frank-Wolfe and Its Variants for Bilevel Optimization

We study Frank-Wolfe (FW) methods for constrained bilevel optimization when the lower-level problem is solved only approximately, yielding biased and inexact hypergradients. We analyze inexact variants of vanilla FW as well as away-step and pairwise FW, and provide convergence rates in the nonconvex setting under gradient errors. By combining these results with recent bounds on hypergradient errors from iterative and approximate implicit differentiation, we derive overall iteration complexity guarantees for bilevel FW. Experiments on two real-world applications validate the theory and demonstrate practical effectiveness.

math.OC↗

arXiv2016

Parallel Strategies Selection

We consider the problem of selecting the best variable-value strategy for solving a given problem in constraint programming. We show that the recent Embarrassingly Parallel Search method (EPS) can be used for this purpose. EPS proposes to solve a problem by decomposing it in a lot of subproblems and to give them on-demand to workers which run in parallel. Our method uses a part of these subproblems as a simple sample as defined in statistics for comparing some strategies in order to select the most promising one that will be used for solving the remaining subproblems. For each subproblem of the sample, the parallelism helps us to control the running time of the strategies because it gives us the possibility to introduce timeouts by stopping a strategy when it requires more than twice the time of the best one. Thus, we can deal with the great disparity in solving times for the strategies. The selections we made are based on the Wilcoxon signed rank tests because no assumption has to be made on the distribution of the solving times and because these tests can deal with the censored data that we obtain after introducing timeouts. The experiments we performed on a set of classical benchmarks for satisfaction and optimization problems show that our method obtain good performance by selecting almost all the time the best variable-value strategy and by almost never choosing a variable-value strategy which is dramatically slower than the best one. Our method also outperforms the portfolio approach consisting in running some strategies in parallel and is competitive with the multi armed bandit framework.

cs.AI↗