Unbiased Least Squares Regression via Averaged Stochastic Gradient Descent
References
- [1] (2018) Unbiased Monte Carlo: Posterior estimation for intractable/infinite-dimensional models. Bernoulli 24(3):1726–1786.Crossref, Google Scholar
- [2] (2021) Stochastic bias-reduced gradient methods. Ranzato M, Beygelzimer A, Dauphin Y, Liang PS, Wortman Vaughan J, eds. Proc. 35th Internat. Conf. Neural Inform. Processing Systems (Curran Associates, Red Hook, NY), 10810–10822.Google Scholar
- [3] (2007) Stochastic Simulation: Algorithms and Analysis, Stochastic Modelling and Applied Probability, vol. 57 (Springer Science & Business Media, New York).Crossref, Google Scholar
- [4] (2013) Non-strongly-convex smooth stochastic approximation with convergence rate O(1/n). Burges CJC, Bottou L, Welling M, Ghahramani Z, Weinberger KO, eds. Proc. 27th Internat. Conf. Neural Inform. Processing Systems (Curran Associates, Red Hook, NY), 773–781.Google Scholar
- [5] (2019) Unbiased multilevel Monte Carlo: Stochastic optimization, steady-state simulation, quantiles, and other applications. Preprint, submitted April 22, https://arxiv.org/abs/1904.09929.Google Scholar
- [6] (2018) Optimization methods for large-scale machine learning. SIAM Rev. 60(2):223–311.Crossref, Google Scholar
- [7] (2021) Unbiased inference for discretely observed hidden Markov model diffusions. SIAM/ASA J. Uncertainty Quantification 9(2):763–787.Crossref, Google Scholar
- [8] (2020) Optimal unbiased estimation for expected cumulative discounted cost. Eur. J. Oper. Res. 286(2):604–618.Crossref, Google Scholar
- [9] (2015) Averaged least-mean-squares: Bias-variance trade-offs and optimal sampling distributions. Lebanon G, Vishwanathan SVN, eds. Proc. 18th Internat. Conf. Artificial Intelligence Statist., Proceedings of the Machine Learning Research, vol. 38 (PMLR, New York), 205–213.Google Scholar
- [10] (2016) Nonparametric stochastic approximation with large step-sizes. Ann. Statist. 44(4):1363–1399.Crossref, Google Scholar
- [11] (2017) Harder, better, faster, stronger convergence rates for least-squares regression. J. Machine Learn. Res. 18(101):1–51.Google Scholar
- [12] (2008) Multilevel Monte Carlo path simulation. Oper. Res. 56(3):607–617.Link, Google Scholar
- [13] (2004) Monte Carlo Methods in Financial Engineering (Springer, New York).Crossref, Google Scholar
- [14] (2014) Exact estimation for Markov chain equilibrium expectations. J. Appl. Probab. 51(A):377–389.Crossref, Google Scholar
- [15] (1992) The asymptotic efficiency of simulation estimators. Oper. Res. 40(3):505–520.Link, Google Scholar
- [16] (2013) Matrix Computations, 4th ed. (JHU Press, Baltimore).Crossref, Google Scholar
- [17] (2020) Variance-reduced methods for machine learning. Proc. IEEE 108(11):1968–1983.Crossref, Google Scholar
- [18] (2024) Online inference with debiased stochastic gradient descent. Biometrika 111(1):93–108.Crossref, Google Scholar
- [19] (2024) On unbiased estimation for partially observed diffusions. J. Machine Learn. Res. 25(66):1–66.Google Scholar
- [20] (2025) On the convergence rate of stochastic approximation for gradient-based stochastic optimization. Oper. Res. 73(2):1143–1150.Link, Google Scholar
- [21] (2018) Accelerating stochastic gradient descent for least squares regression. Bubeck S, Perchet V, Rigollet P, eds. 31st Annual Conf. Learn. Theory, Proceedings of the Machine Learning Research, vol. 75 (PMLR, New York), 545–604.Google Scholar
- [22] (2018) Parallelizing stochastic gradient descent for least squares regression: Mini-batching, averaging, and model misspecification. J. Machine Learn. Res. 18(223):1–42.Google Scholar
- [23] (2020) General multilevel Monte Carlo methods for pricing discretely monitored Asian options. Eur. J. Oper. Res. 287(2):739–748.Crossref, Google Scholar
- [24] (2024) Unbiased time-average estimators for Markov chains. Math. Oper. Res. 49(4):2136–2165.Link, Google Scholar
- [25] (2011) A general method for debiasing a Monte Carlo estimator. Monte Carlo Methods Appl. 17(4):301–315.Crossref, Google Scholar
- [26] (2020) Unbiased Markov chain Monte Carlo for intractable target distributions. Electronic J. Statist. 14(2):2842–2891.Crossref, Google Scholar
- [27] (2022) Exact minimax risk for linear least squares, and the lower tail of sample covariance matrices. Ann. Statist. 50(4):2157–2178.Crossref, Google Scholar
- [28] (2016) Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Math. Programming 155(1):549–573.Crossref, Google Scholar
- [29] (1992) Acceleration of stochastic approximation by averaging. SIAM J. Control Optim. 30(4):838–855.Crossref, Google Scholar
- [30] (2015) Unbiased estimation with square root convergence for SDE models. Oper. Res. 63(5):1026–1043.Link, Google Scholar
- [31] (1988) Efficient estimations from a slowly convergent Robbins-Monro process. Technical report, Cornell University Operations Research and Industrial Engineering, Ithaca, NY.Google Scholar
- [32] (2020) Debiasing averaged stochastic gradient descent to handle missing values. Larochelle H, Ranzato M, Hadsell R, Balcan MF, Lin H, eds. Proc. 34th Internat. Conf. Neural Inform. Processing Systems (Curran Associates, Red Hook, NY), 12957–12967.Google Scholar
- [33] (2021) Last iterate convergence of SGD for least-squares in the interpolation regime. Ranzato M, Beygelzimer A, Dauphin Y, Liang PS, Wortman Vaughan J, eds. Proc. 35th Conf. Neural Inform. Processing Systems (NeurIPS 2021) (Curran Associates, Red Hook, NY), 21581–21591.Google Scholar
- [34] (2018) Unbiased estimators and multilevel Monte Carlo. Oper. Res. 66(2):448–462.Link, Google Scholar
- [35] (2023) Unbiased multilevel Monte Carlo methods for intractable distributions: MLMC meets MCMC. J. Machine Learn. Res. 24(249):1–40.Google Scholar
- [36] (2022) Distributed stochastic optimization with large delays. Math. Oper. Res. 47(3):2082–2111.Link, Google Scholar

