• Corpus ID: 249151855

A gradient estimator via L1-randomization for online zero-order optimization with two point feedback

@inproceedings{Akhavan2022AGE,
  title={A gradient estimator via L1-randomization for online zero-order optimization with two point feedback},
  author={Arya Akhavan and Evgenii Chzhen and Massimiliano Pontil and A. Tsybakov},
  year={2022}
}
This work studies online zero-order optimization of convex and Lipschitz functions. We present a novel gradient estimator based on two function evaluations and randomization on the (cid:96) 1 -sphere. Considering different geometries of feasible sets and Lipschitz assumptions we analyse online dual averaging algorithm with our estimator in place of the usual gradient. We consider two types of assumptions on the noise of the zero-order oracle: canceling noise and adversarial noise. We provide an… 
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References

SHOWING 1-10 OF 33 REFERENCES

Distributed Zero-Order Optimization under Adversarial Noise

We study the problem of distributed zero-order optimization for a class of strongly convex functions. They are formed by the average of local objectives, associated to different nodes in a prescribed…

A Modern Introduction to Online Learning

This monograph introduces the basic concepts of Online Learning through a modern view of Online Convex Optimization, and presents first-order and second-order algorithms for online learning with convex losses, in Euclidean and non-Euclidean settings.

Exploiting Higher Order Smoothness in Derivative-free Optimization and Continuous Bandits

The results imply that the zero-order algorithm is nearly optimal in terms of sample complexity and the problem parameters, and an estimator of the minimum value of the function achieving almost sharp oracle behavior is proposed.

Highly-Smooth Zero-th Order Online Optimization

It is shown that as opposed to gradient-based algorithms, high-order smoothness may be used to improve estimation rates, with a precise dependence of the authors' upper-bounds on the degree of smoothness.

Kernel-based methods for bandit convex optimization

We consider the adversarial convex bandit problem and we build the first poly(T)-time algorithm with poly(n) √T-regret for this problem. To do so we introduce three new ideas in the derivative-free…

Improved Regret Guarantees for Online Smooth Convex Optimization with Bandit Feedback

The first algorithm whose expected regret is O(T ), ignoring constant and logarithmic factors is given, building upon existing work on selfconcordant regularizers and one-point gradient estimation.

On the Complexity of Bandit and Derivative-Free Stochastic Convex Optimization

  • O. Shamir
  • Computer Science, Mathematics
    COLT
  • 2013
The attainable error/regret in the bandit and derivative-free settings, as a function of the dimension d and the available number of queries T is investigated, and a precise characterization of the attainable performance for strongly-convex and smooth functions is provided.

Scale-free online learning

Optimal Rates for Zero-Order Convex Optimization: The Power of Two Function Evaluations

Focusing on nonasymptotic bounds on convergence rates, it is shown that if pairs of function values are available, algorithms for d-dimensional optimization that use gradient estimates based on random perturbations suffer a factor of at most √d in convergence rate over traditional stochastic gradient methods.

Escaping the Local Minima via Simulated Annealing: Optimization of Approximately Convex Functions

We consider the problem of optimizing an approximately convex function over a bounded convex set in $\mathbb{R}^n$ using only function evaluations. The problem is reduced to sampling from an…