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The Limit Points of (Optimistic) Gradient Descent in Min-Max Optimization [article]

Constantinos Daskalakis, Ioannis Panageas
<span title="2018-07-11">2018</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We characterize the limit points of two basic first order methods, namely Gradient Descent/Ascent (GDA) and Optimistic Gradient Descent Ascent (OGDA).  ...  Motivated by applications in Optimization, Game Theory, and the training of Generative Adversarial Networks, the convergence properties of first order methods in min-max problems have received extensive  ...  Our contribution and techniques: In this paper we analyze Gradient Descent/Ascent (GDA) and Optimistic Gradient Descent/Ascent (OGDA) dynamics applied to min-max optimization problems.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1807.03907v1">arXiv:1807.03907v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/7mmpjo7z7za33j2ak6gtd3tpfy">fatcat:7mmpjo7z7za33j2ak6gtd3tpfy</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200910081320/https://arxiv.org/pdf/1807.03907v1.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/75/b3/75b32165fd7d2aa2f9881005db72d5cea1b94d4a.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1807.03907v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Optimistic Distributionally Robust Policy Optimization [article]

Jun Song, Chaoyue Zhao
<span title="2020-06-14">2020</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Moreover, it achieves a globally optimal policy update that is not promised in the prevailing policy based RL algorithms.  ...  as they limit the policy representation to a particular parametric distribution class.  ...  If the initial point β 0 is in [max s,i {A π (s, a ks ) − A π (s, a i )}, +∞), the optimal β solution is max s,i {A π (s, a ks ) − A π (s, a i )}. (2).  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2006.07815v1">arXiv:2006.07815v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/z7rv3jy4njcmdcdpp7ijzpr2qu">fatcat:z7rv3jy4njcmdcdpp7ijzpr2qu</a> </span>
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An Optimistic Acceleration of AMSGrad for Nonconvex Optimization [article]

Jun-Kun Wang, Xiaoyun Li, Belhal Karimi, Ping Li
<span title="2020-11-03">2020</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
In the nonconvex case, we establish a non-asymptotic convergence bound independently of the initialization.  ...  We propose a new variant of AMSGrad, a popular adaptive gradient based optimization algorithm widely used for training deep neural networks.  ...  It combines the idea of adaptive optimization with optimistic learning.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1903.01435v3">arXiv:1903.01435v3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/7aundvaafba5tcqn4disoxpi4u">fatcat:7aundvaafba5tcqn4disoxpi4u</a> </span>
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Calculating Optimistic Likelihoods Using (Geodesically) Convex Optimization [article]

Viet Anh Nguyen, Soroosh Shafieezadeh-Abadeh, Man-Chung Yue, Daniel Kuhn, Wolfram Wiesemann
<span title="2019-10-17">2019</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
A fundamental problem arising in many areas of machine learning is the evaluation of the likelihood of a given observation under different nominal distributions.  ...  We thus propose to replace each nominal distribution with an ambiguity set containing all distributions in its vicinity and to evaluate an optimistic likelihood, that is, the maximum of the likelihood  ...  Acknowledgments We gratefully acknowledge financial support from the Swiss National Science Foundation under grant BSCGI0_157733 as well as the EPSRC grants EP/M028240/1, EP/M027856/1 and EP/N020030/1.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1910.07817v1">arXiv:1910.07817v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/67yjqarrxfd2ro7uutewuryb2a">fatcat:67yjqarrxfd2ro7uutewuryb2a</a> </span>
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A Unified Analysis of Extra-gradient and Optimistic Gradient Methods for Saddle Point Problems: Proximal Point Approach [article]

Aryan Mokhtari, Asuman Ozdaglar, Sarath Pattathil
<span title="2019-09-05">2019</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
In this paper we consider solving saddle point problems using two variants of Gradient Descent-Ascent algorithms, Extra-gradient (EG) and Optimistic Gradient Descent Ascent (OGDA) methods.  ...  We show that both of these algorithms admit a unified analysis as approximations of the classical proximal point method for solving saddle point problems.  ...  and , extra-gradient (EG), optimistic gradient descent ascent (OGDA), and gradient descent ascent (GDA) for min x max y xy.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1901.08511v4">arXiv:1901.08511v4</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/54tzuc4ux5fvhpg6o6avnuq3bu">fatcat:54tzuc4ux5fvhpg6o6avnuq3bu</a> </span>
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Optimistic mirror descent in saddle-point problems: Going the extra (gradient) mile [article]

Panayotis Mertikopoulos and Bruno Lecouat and Houssam Zenati and Chuan-Sheng Foo and Vijay Chandrasekhar and Georgios Piliouras
<span title="2018-10-01">2018</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We then show that this deficiency is mitigated by optimism: by taking an "extra-gradient" step, optimistic mirror descent (OMD) converges in all coherent problems.  ...  Our analysis generalizes and extends the results of Daskalakis et al. (2018) for optimistic gradient descent (OGD) in bilinear problems, and makes concrete headway for establishing convergence beyond convex-concave  ...  In particular, Daskalakis et al. ( ) showed that optimistic gradient descent (OGD) succeeds in cases where vanilla gradient descent (GD) fails (speci cally, unconstrained bilinear saddle-point problems  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1807.02629v2">arXiv:1807.02629v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/va6lywidcfh5xojmoqjgo4nzry">fatcat:va6lywidcfh5xojmoqjgo4nzry</a> </span>
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Mix and Match: An Optimistic Tree-Search Approach for Learning Models from Mixture Distributions [article]

Matthew Faw, Rajat Sen, Karthikeyan Shanmugam, Constantine Caramanis, Sanjay Shakkottai
<span title="2020-07-14">2020</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Our proposed algorithm, Mix&Match, combines stochastic gradient descent (SGD) with optimistic tree search and model re-use (evolving partially trained models with samples from different mixture distributions  ...  We prove simple regret guarantees for our algorithm with respect to recovering the optimal mixture, given a total budget of SGD evaluations.  ...  the feasible set of w and do not run projected gradient descent, a convergence guarantee of the formÕ Ḡ t that follows from a uniform bound on the stochastic gradient does not suffice in our setting becauseḠ  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1907.10154v5">arXiv:1907.10154v5</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/b4smmwskvffrvpsd5qz466ohwq">fatcat:b4smmwskvffrvpsd5qz466ohwq</a> </span>
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On the modes of convergence of Stochastic Optimistic Mirror Descent (OMD) for saddle point problems [article]

Yanting Ma, Shuchin Aeron, Hassan Mansour
<span title="2019-08-02">2019</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
In this article, we study the convergence of Mirror Descent (MD) and Optimistic Mirror Descent (OMD) for saddle point problems satisfying the notion of coherence as proposed in Mertikopoulos et al.  ...  This is in contrast to the claim in Mertikopoulos et al. of monotone convergence of OMD with exact gradients for coherent saddle point problems.  ...  In particular these papers consider the following general saddle-point (SP) problem. min x 1 ∈X 1 max x 2 ∈X 2 f (x 1 , x 2 ), (1) where X i are compact convex subset of a finite-dimensional normed space  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1908.01071v1">arXiv:1908.01071v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/xsg57bhho5f5jpdcmqjohfmahy">fatcat:xsg57bhho5f5jpdcmqjohfmahy</a> </span>
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Optimistic Regret Minimization for Extensive-Form Games via Dilated Distance-Generating Functions [article]

Gabriele Farina and Christian Kroer and Tuomas Sandholm
<span title="2019-10-28">2019</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Furthermore, we show that the use of dilated distance-generating functions enable us to decompose the mirror descent algorithm, and its optimistic variant, into local mirror descent algorithms at each  ...  We study the performance of optimistic regret-minimization algorithms for both minimizing regret in, and computing Nash equilibria of, zero-sum extensive-form games.  ...  Acknowledgments This material is based on work supported by the National Science Foundation under grants IIS-1718457, IIS-1617590, and CCF-1733556, and the ARO under award W911NF-17-1-0082.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1910.10906v2">arXiv:1910.10906v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/umg5iz4iqnhlfddlrjwywxpave">fatcat:umg5iz4iqnhlfddlrjwywxpave</a> </span>
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Optimistic Dual Extrapolation for Coherent Non-monotone Variational Inequalities [article]

Chaobing Song, Zhengyuan Zhou, Yichao Zhou, Yong Jiang, Yi Ma
<span title="2021-03-07">2021</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
In this paper, we propose optimistic dual extrapolation (OptDE), a method that only performs one gradient evaluation per iteration.  ...  In particular, when a weak solution exists, the convergence rate of our method is O(1/ϵ^2), which matches the best existing result of the methods with two gradient evaluations.  ...  In terms of single-call methods for minimax problems, vanilla gradient descent ascent (and its mirror descent generalizations) might be a natural choice.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2103.04410v1">arXiv:2103.04410v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/qvavrg6l2ffq3biz3hmrdmeb2e">fatcat:qvavrg6l2ffq3biz3hmrdmeb2e</a> </span>
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Last-iterate Convergence of Decentralized Optimistic Gradient Descent/Ascent in Infinite-horizon Competitive Markov Games [article]

Chen-Yu Wei, Chung-Wei Lee, Mengxiao Zhang, Haipeng Luo
<span title="2021-07-07">2021</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Our algorithm is based on running an Optimistic Gradient Descent Ascent algorithm on each state to learn the policies, with a critic that slowly learns the value of each state.  ...  to the set of Nash equilibria under self-play), agnostic (no need to know the actions played by the opponent), symmetric (players taking symmetric roles in the algorithm), and enjoying a finite-time last-iterate  ...  A unified analysis of extra-gradient and optimistic gradient methods for saddle point problems: Proximal point approach. International Conference on Artificial Intelligence and Statistics, 2020.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2102.04540v2">arXiv:2102.04540v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/v7ydahbfo5arpiw2vbailymxaa">fatcat:v7ydahbfo5arpiw2vbailymxaa</a> </span>
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Optimistic Exploration even with a Pessimistic Initialisation [article]

Tabish Rashid, Bei Peng, Wendelin Böhmer, Shimon Whiteson
<span title="2020-02-26">2020</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We propose a simple count-based augmentation to pessimistically initialised Q-values that separates the source of optimism from the neural network.  ...  Our algorithm, Optimistic Pessimistically Initialised Q-Learning (OPIQ), augments the Q-value estimates of a DQN-based agent with count-derived bonuses to ensure optimism during both action selection and  ...  OPIQ, on the other hand, is designed with these limitations of neural networks in mind.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2002.12174v1">arXiv:2002.12174v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/opbdvgo3qrep5n2gy4i765acb4">fatcat:opbdvgo3qrep5n2gy4i765acb4</a> </span>
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The route to chaos in routing games: When is Price of Anarchy too optimistic? [article]

Thiparat Chotibut, Fryderyk Falniowski, Michał Misiurewicz, Georgios Piliouras
<span title="2019-11-24">2019</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Although the Price of Anarchy is equal to one, in the large population limit the time-average social cost for all but a zero measure set of initial conditions converges to its worst possible value.  ...  If the equilibrium flow is a symmetric 50-50% split, the system exhibits one period-doubling bifurcation. A single periodic attractor of period two replaces the attracting fixed point.  ...  Despite this divergent, chaotic behavior, gradient descent with fixed step size, has vanishing regret in zero-sum games [7] .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1906.02486v2">arXiv:1906.02486v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/tbsgjgv57fhbletfa7hopzof3e">fatcat:tbsgjgv57fhbletfa7hopzof3e</a> </span>
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Efficient Optimistic Exploration in Linear-Quadratic Regulators via Lagrangian Relaxation [article]

Marc Abeille, Alessandro Lazaric
<span title="2020-07-13">2020</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Inspired by the extended value iteration algorithm used in optimistic algorithms for finite MDPs, we propose to relax the optimistic optimization of and cast it into a constrained extended LQR problem,  ...  To the best of our knowledge, this is the first computationally efficient confidence-based algorithm for LQR with worst-case optimal regret guarantees.  ...  Given the last point of Lem. 5, this means that despite returning an -optimal solution in the sense of ( 21 ), π µ l may significantly violate the constraint (as D (µ l ) = g πµ l = Ω(1)).  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2007.06482v1">arXiv:2007.06482v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/kurm6k3x2feu5dtmwccgiwk3by">fatcat:kurm6k3x2feu5dtmwccgiwk3by</a> </span>
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Tight Last-Iterate Convergence of the Extragradient and the Optimistic Gradient Descent-Ascent Algorithm for Constrained Monotone Variational Inequalities [article]

Yang Cai, Argyris Oikonomou, Weiqiang Zheng
<span title="2022-05-16">2022</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We use the tangent residual (or a slight variation of the tangent residual) as the the potential function in our analysis of the extragradient algorithm (or the optimistic gradient descent-ascent algorithm  ...  What is the last-iterate convergence rate of the extragradient algorithm or the optimistic gradient descent-ascent algorithm for monotone and Lipschitz variational inequalities with constraints?  ...  Let z k and w k be the k-th iterate of the Optimistic Gradient Descent Ascent Method (OGDA) method. Let z 0 , w 0 be arbitrary starting points in Z.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2204.09228v3">arXiv:2204.09228v3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ofgxwdyakzbszawzwvzdo5pghe">fatcat:ofgxwdyakzbszawzwvzdo5pghe</a> </span>
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