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Oracle lower bounds for stochastic gradient sampling algorithms

Published:2022-05-01 Issue:2 Volume:28 Page:
ISSN:1350-7265
Container-title:Bernoulli
language:
Short-container-title:Bernoulli

Author:

Chatterji Niladri S.¹,Bartlett Peter L.²,Long Philip M.³

Affiliation:

1. Department of Computer Science, Stanford University, 353 Jane Stanford Way, Stanford, CA 94305, USA

2. University of California, Berkeley & Google, 367 Evans Hall #3860, Berkeley, CA 94720-3860, USA

3. Google, 1600 Amphitheatre Parkway, Mountain View, CA, 94043, USA

Publisher

Bernoulli Society for Mathematical Statistics and Probability

Subject

Statistics and Probability

Reference50 articles.

1. Brooks, S., Gelman, A., Jones, G.L. and Meng, X.-L., eds. (2011). Handbook of Markov Chain Monte Carlo. Chapman & Hall/CRC Handbooks of Modern Statistical Methods. Boca Raton, FL: CRC Press.

2. Mengersen, K.L. and Tweedie, R.L. (1996). Rates of convergence of the Hastings and Metropolis algorithms. Ann. Statist. 24 101–121.

3. Wainwright, M.J. (2019). High-Dimensional Statistics: A Non-asymptotic Viewpoint. Cambridge Series in Statistical and Probabilistic Mathematics 48. Cambridge: Cambridge Univ. Press.

4. Agarwal, A., Bartlett, P.L., Ravikumar, P. and Wainwright, M.J. (2012). Information-theoretic lower bounds on the oracle complexity of stochastic convex optimization. IEEE Trans. Inf. Theory 58 3235–3249.

5. Bélisle, C.J.P., Romeijn, H.E. and Smith, R.L. (1993). Hit-and-run algorithms for generating multivariate distributions. Math. Oper. Res. 18 255–266.

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