Adaptive, Doubly Optimal No-Regret Learning in Strongly Monotone and Exp-Concave Games with Gradient Feedback
References
- (2008) Optimal strategies and minimax lower bounds for online convex games. COLT (Omnipress, Madison, MI), 414–424.Google Scholar
- (2022) Stochastic variance reduction for variational inequality methods. COLT (PMLR, New York), 778–816.Google Scholar
- (2021) Adaptive extra-gradient methods for min-max optimization and games. ICLR, 1–12.Google Scholar
- Ba W, Lin T, Zhang J, Zhou Z (2021) Doubly optimal no-regret online learning in strongly monotone games with bandit feedback. Preprint, submitted December 6, https://arxiv.org/abs/2112.02856.Google Scholar
- (2021) Optimal dynamic regret in exp-concave online learning. COLT (PMLR, New York), 359–409.Google Scholar
- (2022) Optimal dynamic regret in proper online learning with strongly convex losses and beyond. AISTATS (PMLR, New York), 1805–1845.Google Scholar
- (2019) A universal algorithm for variational inequalities adaptive to smoothness and noise. COLT (PMLR, New York), 164–194.Google Scholar
- (2016) Stochastic variance reduction methods for saddle-point problems. NIPS, 1416–1424.Google Scholar
- (2016) Minimizing regret on reflexive Banach spaces and Nash equilibria in continuous zero-sum games. NIPS, 154–162.Google Scholar
- (2011) Convex Analysis and Monotone Operator Theory in Hilbert Spaces, vol. 408 (Springer, Berlin, Heidelberg).Crossref, Google Scholar
- (2015) Non-stationary stochastic optimization. Oper. Res. 63(5):1227–1244.Link, Google Scholar
- (2015) Evolutionary dynamics of multi-agent learning: A survey. J. Artificial Intelligence Res. 53:659–697.Crossref, Google Scholar
- (1998) Online algorithms in machine learning. Online Algorithms (Springer, Berlin, Heidelberg), 306–325.Crossref, Google Scholar
- (2007) From external to internal regret. J. Machine Learn. Res. 8(6):1307–1324.Google Scholar
- (2018) Bandit learning in concave N-person games. NeurIPS, 5661–5671.Google Scholar
- (2021) Kernel-based methods for bandit convex optimization. J. ACM 68(4):1–35.Crossref, Google Scholar
- (2022) Finite-time last-iterate convergence for learning in multi-player games. NeurIPS, 33904–33919.Google Scholar
- (2006) Prediction, Learning, and Games (Cambridge University Press, Cambridge, UK).Crossref, Google Scholar
- (2017) Accelerated schemes for a class of variational inequalities. Math. Programming 165:113–149.Crossref, Google Scholar
- (1991) Universal portfolios. Math. Finance 1(1):1–29.Crossref, Google Scholar
- (1999) Elements of Information Theory (John Wiley & Sons, Hoboken, NJ).Google Scholar
- (2020a) Better full-matrix regret via parameter-free online learning. NeurIPS, 8836–8846.Google Scholar
- (2020b) Parameter-free, dynamic, and strongly-adaptive online learning. ICML (PMLR, New York), 2250–2259.Google Scholar
- (2018) Black-box reductions for parameter-free online learning in Banach spaces. COLT (PMLR, New York), 1493–1529.Google Scholar
- (2015) Strongly adaptive online learning. ICML, 1405–1411.Google Scholar
- (1952) A social equilibrium existence theorem. Proc. Natl. Acad. Sci. USA 38(10):886–893.Crossref, Google Scholar
- (2014) SAGA: A fast incremental gradient method with support for non-strongly convex composite objectives. NIPS, 1646–1654.Google Scholar
- (2011) Adaptive subgradient methods for online learning and stochastic optimization. J. Machine Learn. Res. 12(61):2121–2159.Google Scholar
- (2007) Finite-Dimensional Variational Inequalities and Complementarity Problems (Springer Science & Business Media, Berlin, Heidelberg).Google Scholar
- (2002) Stochastic Portfolio Theory, vol. 48 (Springer Science & Business Media, Berlin, Heidelberg).Crossref, Google Scholar
- (2005) Online convex optimization in the bandit setting: Gradient descent without a gradient. SODA, 385–394.Google Scholar
- (2015) Adaptive online learning. NeurIPS, 3375–3383.Google Scholar
- (2017) Parameter-free online learning via model selection. NeurIPS, 6022–6032.Google Scholar
- (2022) New projection-free algorithms for online convex optimization with adaptive regret guarantees. COLT (PMLR, New York), 2326–2359.Google Scholar
- (2005) Wireless Communications (Cambridge University Press, Cambridge, UK).Crossref, Google Scholar
- (2020) Tight last-iterate convergence rates for no-regret learning in multi-player games. NeurIPS, 20766–20778.Google Scholar
- (2016) Introduction to Online Convex Optimization (MIT Press, Cambridge, MA), 157–325.Google Scholar
- (2019) Revisiting the Polyak step size. Preprint, submitted May 1, https://arxiv.org/abs/1905.00313.Google Scholar
- (2014) Beyond the regret minimization barrier: Optimal algorithms for stochastic strongly-convex optimization. J. Machine Learn. Res. 15(1):2489–2512.Google Scholar
- (2007) Adaptive algorithms for online decision problems. ECCC 14(88).Google Scholar
- (2007) Logarithmic regret algorithms for online convex optimization. Machine Learn. 69(2–3):169–192.Crossref, Google Scholar
- (2014) Logistic regression: Tight bounds for stochastic and online optimization. COLT (PMLR, New York), 197–209.Google Scholar
- (2021) Adaptive learning in continuous games: Optimal regret bounds and convergence to Nash equilibrium. COLT (PMLR, New York), 2388–2422.Google Scholar
- (2022) New first-order algorithms for stochastic variational inequalities. SIAM J. Optim. 32(4):2745–2772.Crossref, Google Scholar
- (2022) An accelerated variance reduced extrapoint approach to finite-sum VI and optimization. Preprint, submitted November 7, https://arxiv.org/abs/2211.03269.Google Scholar
- (2009) A nonparametric asymptotic analysis of inventory planning with censored demand. Math. Oper. Res. 34(1):103–123.Link, Google Scholar
- (2017) Extragradient method with variance reduction for stochastic variational inequalities. SIAM J. Optim. 27(2):686–724.Crossref, Google Scholar
- (2019) Variance-based extragradient methods with line search for stochastic variational inequalities. SIAM J. Optim. 29(1):175–206.Crossref, Google Scholar
- (2015) Online optimization: Competing with dynamic comparators. AISTATS (PMLR, New York), 398–406.Google Scholar
- (2019) A proximal-point algorithm with variable sample-sizes (PPAWSS) for monotone stochastic variational inequality problems. WSC (IEEE, Piscataway, NJ), 3551–3562.Google Scholar
- (2008) Stochastic approximation approaches to the stochastic variational inequality problem. IEEE Trans. Automatic Control 53(6):1462–1475.Crossref, Google Scholar
- (2022) Sharper rates for separable minimax and finite sum optimization via primal-dual extragradient methods. COLT (PMLR, New York), 4362–4415.Google Scholar
- (2013) Accelerating stochastic gradient descent using predictive variance reduction. NIPS, 315–323.Google Scholar
- (2011) Solving variational inequalities with stochastic mirror-prox algorithm. Stochastic Systems 1(1):17–58.Link, Google Scholar
- (2008) Learning by mirror averaging. Ann. Statist. 36(5):2183–2206.Crossref, Google Scholar
- (2019) Parameter-free online convex optimization with sub-exponential noise. COLT (PMLR, New York), 1802–1823.Google Scholar
- (2017a) Improved strongly adaptive online learning using coin betting. AISTATS (PMLR, New York), 943–951.Google Scholar
- (2017b) Online learning for changing environments using coin betting. Electronic J. Statist. 11(2):5282–5310.Crossref, Google Scholar
- (2021) Dynamic online learning via Frank-Wolfe algorithm. IEEE Trans. Signal Processing 69:932–947.Crossref, Google Scholar
- (2019) Optimal stochastic extragradient schemes for pseudomonotone stochastic variational inequality problems and their variants. Comput. Optim. Appl. 74(3):779–820.Crossref, Google Scholar
- (2015) Adam: A method for stochastic optimization. ICLR, 1–15.Google Scholar
- (1999) Averaging expert predictions. EuroCOLT (Springer, Berlin, Heidelberg), 153–167.Google Scholar
- (2015) Fast rates for exp-concave empirical risk minimization. NeurIPS, 1477–1485.Google Scholar
- (2012) Regularized iterative stochastic approximation methods for stochastic variational inequality problems. IEEE Trans. Automatic Control 58(3):594–609.Crossref, Google Scholar
- (2022) Simple and optimal methods for stochastic variational inequalities, I: Operator extrapolation. SIAM J. Optim. 32(3):2041–2073.Crossref, Google Scholar
- (2015) Convergence of heterogeneous distributed learning in stochastic routing games. Allerton (IEEE, Piscataway, NJ), 480–487.Google Scholar
- (2017) Less than a single pass: Stochastically controlled stochastic gradient. AISTATS (PMLR, New York), 148–156.Google Scholar
- (2020) On the adaptivity of stochastic gradient-based optimization. SIAM J. Optim. 30(2):1473–1500.Crossref, Google Scholar
- (2017) Online to offline conversions, universality and adaptive minibatch sizes. NeurIPS, 1612–1621.Google Scholar
- (2018) Online adaptive methods, universality and acceleration. NeurIPS, 6501–6510.Google Scholar
- (2019) On the convergence of stochastic gradient descent with adaptive stepsizes. AISTATS (PMLR, New York), 983–992.Google Scholar
- (2020) Finite-time last-iterate convergence for multi-agent learning in games. ICML (PMLR, New York), 6161–6171.Google Scholar
- (2021) Stochastic gradient descent-ascent and consensus optimization for smooth games: Convergence analysis under expected co-coercivity. NeurIPS, 19095–19108.Google Scholar
- (2023) Projection-free adaptive regret with membership oracles. ALT (PMLR, New York), 1055–1073.Google Scholar
- (2016) Efficient second order online learning by sketching. NeurIPS, 902–910.Google Scholar
- (2015) Lower and upper bounds on the generalization of stochastic exponentially concave optimization. COLT (PMLR, New York), 1305–1320.Google Scholar
- (2019) Learning in games with continuous action sets and unknown payoff functions. Math. Programming 173(1–2):465–507.Crossref, Google Scholar
- (2018) Cycles in adversarial regularized learning. SODA (SIAM, Philadelphia, PA), 2703–2717.Google Scholar
- (2019) Optimistic mirror descent in saddle-point problems: Going the extra(-gradient) mile. ICLR, 1–23.Google Scholar
- (2016) Online optimization in dynamic environments: Improved regret rates for strongly convex problems. CDC (IEEE, Piscataway, NJ), 7195–7201.Google Scholar
- (2017) Limits and limitations of no-regret learning in games. Knowledge Engrg. Rev. 32:e21.Crossref, Google Scholar
- (2017) Variants of RMSProp and Adagrad with logarithmic regret bounds. ICML (PMLR, New York), 2545–2553.Google Scholar
- (2004) Prox-method with rate of convergence o(1/t) for variational inequalities with Lipschitz continuous monotone operators and smooth convex-concave saddle point problems. SIAM J. Optim. 15(1):229–251.Crossref, Google Scholar
- (1983) Problem Complexity and Method Efficiency in Optimization (Wiley, Hoboken, NJ).Google Scholar
- (2018) Lectures on Convex Optimization, vol. 137 (Springer, Berlin, Heidelberg).Crossref, Google Scholar
- (2003) Centralized and competitive inventory models with demand substitution. Oper. Res. 51(2):329–335.Link, Google Scholar
- (2022) Finite-sum smooth optimization with SARAH. Comput. Optim. Appl. 82(3):561–593.Crossref, Google Scholar
- (2016) Coin betting and parameter-free online learning. NeurIPS, 577–585.Google Scholar
- (1993) Competitive routing in multiuser communication networks. IEEE/ACM Trans. Networking 1(5):510–521.Crossref, Google Scholar
- (1998) The cost of achieving the best portfolio in hindsight. Math. Oper. Res. 23(4):960–982.Link, Google Scholar
- (1994) A Course in Game Theory (MIT Press, Cambridge, MA).Google Scholar
- (2018) Exponentially concave functions and a new information geometry. Ann. Probab. 46(2):1070–1113.Crossref, Google Scholar
- (1987) Introduction to Optimization (Optimization Software).Google Scholar
- (2001) Wireless Communications: Principles and Practice (Prentice Hall PTR, Hoboken, NJ).Google Scholar
- (2018) On the convergence of Adam and beyond. ICLR, 1–23.Google Scholar
- (2019) Solving monotone stochastic variational inequalities and complementarity problems by progressive hedging. Math. Programming 174(1–2):453–471.Crossref, Google Scholar
- (2017) Stochastic variational inequalities: Single-stage to multistage. Math. Programming 165(1):331–360.Crossref, Google Scholar
- (1965) Existence and uniqueness of equilibrium points for concave N-person games. Econometrica 33(3):520–534.Crossref, Google Scholar
- (2012) A stochastic gradient method with an exponential convergence rate for finite training sets. NIPS, 2663–2671.Google Scholar
- (2015) Population games and deterministic evolutionary dynamics. Handbook of Game Theory with Economic Applications, vol. 4 (Elsevier, Amsterdam), 703–778.Crossref, Google Scholar
- (2012) Online learning and online convex optimization. Foundations Trends Machine Learn. 4(2):107–194.Google Scholar
- (2013) Stochastic variational inequality problems: Applications, analysis, and algorithms. Theory Driven by Influential Applications (INFORMS, Catonsville, MD), 71–107.Google Scholar
- (2008) Multiagent Systems: Algorithmic, Game-Theoretic, and Logical Foundations (Cambridge University Press, Cambridge, UK).Crossref, Google Scholar
- (2016) Finite composite games: Equilibria and dynamics. J. Dynamic Games 3(1):101–120.Crossref, Google Scholar
- (2014) Wireless network optimization by Perron-Frobenius theory. CISS (IEEE, Piscataway, NJ), 1–6.Google Scholar
- (2019) Painless stochastic gradient: Interpolation, line-search, and convergence rates. NIPS, 3732–3745.Google Scholar
- (2009) Optimal Transport: Old and New, vol. 338 (Springer Science & Business Media, Berlin, Heidelberg).Crossref, Google Scholar
- (2013) No-regret dynamics and fictitious play. J. Econom. Theory 148(2):825–842.Crossref, Google Scholar
- (1997) Competitive online linear regression. NIPS, 364–370.Google Scholar
- (2021) Projection-free online learning in dynamic environments. AAAI, 10067–10075.Google Scholar
- (2023) Improved dynamic regret for online Frank-Wolfe. Preprint, submitted February 11, https://arxiv.org/abs/2302.05620.Google Scholar
- (2020) SAdam: A variant of Adam for strongly convex functions. ICLR, 1–21.Google Scholar
- (2019) AdaGrad stepsizes: Sharp convergence over nonconvex landscapes. ICML (PMLR, New York), 6677–6686.Google Scholar
- (2012) Weighted Sum-Rate Maximization in Wireless Networks: A Review (Now Foundations and Trends, Piscataway, NJ).Google Scholar
- (2017) Adaptive SVRG methods under error bound conditions with unknown growth parameter. NIPS, 3279–3289.Google Scholar
- (2018) A simple analysis for exp-concave empirical minimization with arbitrary convex regularizer. AISTATS, 445–453.Google Scholar
- (2016) Tracking slowly moving clairvoyant: Optimal dynamic regret of online learning with true and noisy gradient. ICML (PMLR, New York), 449–457.Google Scholar
- (2013) A regularized smoothing stochastic approximation (RSSA) algorithm for stochastic variational inequality problems. WSC (IEEE, Piscataway, NJ), 933–944.Google Scholar
- (2014) Optimal robust smoothing extragradient algorithms for stochastic variational inequality problems. CDC (IEEE, Piscataway, NJ), 5831–5836.Google Scholar
- (2022) Fast distributionally robust learning with variance-reduced min-max optimization. AISTATS (PMLR, New York), 1219–1250.Google Scholar
- (2019) Adaptive regret of convex and smooth functions. ICML (PMLR, New York), 7414–7423.Google Scholar
- (2018a) Adaptive online learning in dynamic environments. NIPS, 1330–1340.Google Scholar
- (2018b) Dynamic regret of strongly adaptive methods. ICML (PMLR, New York), 5882–5891.Google Scholar
- (2017) Mirror descent learning in continuous games. CDC (IEEE, Piscataway, NJ), 5776–5783.Google Scholar
- (2021) Robust power management via learning and game design. Oper. Res. 69(1):331–345.Link, Google Scholar
- (2018) Learning in games with lossy feedback. NIPS, 1–11.Google Scholar
- (2003) Online convex programming and generalized infinitesimal gradient ascent. ICML, 928–936.Google Scholar
- (2019) A sufficient condition for convergences of Adam and RMSProp. CVPR, 11127–11135.Google Scholar

