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Near-Optimal Algorithms for Minimax Optimization
[article]
2021
arXiv
pre-print
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This paper resolves a longstanding open question pertaining to the design of near-optimal first-order algorithms for smooth and strongly-convex-strongly-concave minimax problems. ...
Our algorithm is designed based on an accelerated proximal point method and an accelerated solver for minimax proximal steps. ...
Most existing work on minimax optimization focuses on the convex-concave setting, where the function f (·, y) is convex for each y ∈ R n and the function f (x, ·) is concave for each x ∈ R m . ...
arXiv:2002.02417v6
fatcat:xppwvgbeafh57g2xdadnv3qmay
Near-Optimal Algorithms for Making the Gradient Small in Stochastic Minimax Optimization
[article]
2022
arXiv
pre-print
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We study the problem of finding a near-stationary point for smooth minimax optimization. ...
We show that the RAIN achieves near-optimal stochastic first-order oracle (SFO) complexity for stochastic minimax optimization in both convex-concave and strongly-convex-strongly-concave cases. ...
To the best of our knowledge, RAIN is the first near-optimal SFO algorithm for finding near-stationary point of stochastic convex-concave minimax problem. ...
arXiv:2208.05925v3
fatcat:2wc5sls53reg7n34tnbmuofshu
Near Optimal Stochastic Algorithms for Finite-Sum Unbalanced Convex-Concave Minimax Optimization
[article]
2022
arXiv
pre-print
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This upper bound is near optimal with respect to ε, n, κ_x and κ_y simultaneously. In addition, the algorithm is easily implemented and works well in practical. ...
Our methods can be extended to solve more general unbalanced convex-concave minimax problems and the corresponding upper complexity bounds are also near optimal. ...
We have shown the optimality of L-SVRE for balanced SCSC minimax and proposed a near optimal algorithm AL-SVRE for unbalanced problems. ...
arXiv:2106.01761v2
fatcat:bkve4vwvarhahoab5544ga7yny
A minimax near-optimal algorithm for adaptive rejection sampling
[article]
2018
arXiv
pre-print
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We give the first theoretical lower bound for the problem of adaptive rejection sampling and introduce a new algorithm which guarantees a near-optimal rejection rate in a minimax sense. ...
This leads to an average rejection rate for NNARS which is minimax near-optimal (up to a logarithmic term) over the class of Hölder densities. ...
This rejection rate is near-optimal, in the minimax sense over the class of s-Hölder smooth densities. ...
arXiv:1810.09390v1
fatcat:cpixwtugqrbh3jc6rb4ea3dml4
New Algorithms for Network Optimization
1973
1973 IEEE G-MTT International Microwave Symposium
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Unlike
previous
work by the authors
[1], where a single optimization
is carried
out with large @ in an effort to reach near minimax
results,
these algorithms
can be described as true minimax ...
CONCLUSIONS
Two new algorithms
for computer-aided
minimax
optimiz-
ation
have been presented
and discussed. ...
doi:10.1109/gmtt.1973.1123085
fatcat:4cyc6wde7fcutnksmhpdlgg3cm
New Algorithms for Network Optimization
1973
IEEE transactions on microwave theory and techniques
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Unlike
previous
work by the authors
[1], where a single optimization
is carried
out with large @ in an effort to reach near minimax
results,
these algorithms
can be described as true minimax ...
CONCLUSIONS
Two new algorithms
for computer-aided
minimax
optimiz-
ation
have been presented
and discussed. ...
doi:10.1109/tmtt.1973.1128137
fatcat:slkfcmg3o5dh5gtmjo4ximteru
A Catalyst Framework for Minimax Optimization
2020
Neural Information Processing Systems
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Despite its simplicity, this leads to a family of near-optimal algorithms with improved complexity over all existing methods designed for strongly-convex-concave minimax problems. ...
We introduce a generic two-loop scheme for smooth minimax optimization with strongly-convex-concave objectives. ...
Based on the generic Catalyst framework, we establish a number of interesting results: (i) For strongly-convex-concave minimax optimization, we develop a family of two-loop algorithms with near-optimal ...
dblp:conf/nips/YangZKH20
fatcat:2ebpuvfnbzajfcj6forpspdxba
Hierarchical Population Game Models of Coevolution in Multi-Criteria Optimization Problems under Uncertainty
2021
Applied Sciences
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The principles of vector minimax and vector minimax risk are used as the basic principles of optimality for the problem of multi-criteria optimization under uncertainty. ...
The article develops hierarchical population game models of co-evolutionary algorithms for solving the problem of multi-criteria optimization under uncertainty. ...
Optimization under Uncertainty
Algorithm of Hierarchical Coevolution Search for Set of -Minimax Solutions to the MOU Problem The proposed algorithm includes the following main steps. ...
doi:10.3390/app11146563
fatcat:diutadsujjf4hc36jsikrfziem
Preserving Privacy of Continuous High-dimensional Data with Minimax Filters
2015
International Conference on Artificial Intelligence and Statistics
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Minimax filters that achieve the optimal privacyutility trade-off from broad families of filters and loss/classifiers are defined, and algorithms for learning the filers in batch or distributed settings ...
Experiments with several real-world tasks including facial expression recognition, speech emotion recognition, and activity recognition from motion, show that the minimax filter can simultaneously achieve ...
Algorithms to find minimax filters are presented in Section 2, which builds on a classic method of minimax optimization (see [18] for a review). ...
dblp:conf/aistats/Hamm15
fatcat:jxf6rrladzel3gtmovxaj3icky
An analysis of optimistic, best-first search for minimax sequential decision making
2014
2014 IEEE Symposium on Adaptive Dynamic Programming and Reinforcement Learning (ADPRL)
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The importance of the effective branching factor in the analysis of minimax algorithms was understood as early as [8], ...
An asymptotic branching factor is defined as a measure of problem complexity, and it is used to characterize the relationship between computation invested and near-optimality. ...
In applications to different problems, the optimistic paradigm has led to some good algorithms, e.g. for optimization [15] , for optimal control of discrete-actions deterministic systems [7] or stochastic ...
doi:10.1109/adprl.2014.7010615
dblp:conf/adprl/BusoniuMP14
fatcat:pvn4z72bfvbfxgug7k6mcsontm
Singularities in minimax optimization of networks
1976
IEEE Transactions on Circuits and Systems
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Based on the theoretical results presented au algorithm for nonlinear minimax optimization is developed. ...
Abssirucr-A theoretical treatment of singularities in nonlinear minimax optimization problems, which allows for a classification in regular and sing&r problems, is presented. ...
Based on the theoretical results presented au algorithm for nonlinear minimax optimization is developed. ...
doi:10.1109/tcs.1976.1084240
fatcat:ow7no3x2bvae7k6t4pk5pbgsiy
Open Problem: Do Good Algorithms Necessarily Query Bad Points?
2019
Annual Conference Computational Learning Theory
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averaging (Ruppert, 1988; Polyak and Juditsky, 1992) for classes of stochastic convex optimization. ...
Folklore results in the theory of Stochastic Approximation indicates the (minimax) optimality of Stochastic Gradient Descent (SGD) (Robbins and Monro, 1951) with polynomially decaying step sizes and iterate ...
of the query points for classes of SGD style algorithms. ...
dblp:conf/colt/00010KKNN19
fatcat:iuls3idev5autnqkbzxsvqxvry
Automated minimax design of networks
1976
Computer-Aided Design
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Nielsen is gratefully acknowledged for having supplied measured data of the device. ...
Recent work by Bandler and Charalambous [S], [6] used at least pth approach together with a gradient optimization algorithm to provide minimax solutions. ...
CONCLUSION A nonlinear minimax optimization method has been developed and documented. ...
doi:10.1016/0010-4485(76)90070-1
fatcat:bhez6ie22faildpap6ch34osxq
Automated minimax design of networks
1975
IEEE Transactions on Circuits and Systems
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Nielsen is gratefully acknowledged for having supplied measured data of the device. ...
Recent work by Bandler and Charalambous [S], [6] used at least pth approach together with a gradient optimization algorithm to provide minimax solutions. ...
CONCLUSION A nonlinear minimax optimization method has been developed and documented. ...
doi:10.1109/tcs.1975.1083973
fatcat:vwtr2fwacjggna6wwwd526x4jy
Near-optimal control of nonlinear switched systems with non-cooperative switching rules
2017
2017 American Control Conference (ACC)
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For any combination of dwell times, OMSδ returns a sequence of switches that is provably near-optimal, and can be applied in receding horizon for closed loop control. ...
The algorithm solves a minimax problem where the controlled signal is chosen to optimize a discounted sum of rewards, while taking into account the worst possible uncontrolled switches. ...
It returns a near-optimal sequence with respect to the minimax-optimal value. ...
doi:10.23919/acc.2017.7963352
dblp:conf/amcc/RejebBMD17
fatcat:cbcgnriafbb4nkfxvqedbyim2y
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