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Optimistic and Adaptive Lagrangian Hedging [article]

Ryan D'Orazio, Ruitong Huang
2021 arXiv   pre-print
In this work we introduce optimism and adaptive stepsizes to Lagrangian hedging, a class of online algorithms that includes regret-matching, and hedge (i.e. multiplicative weights).  ...  Our results include: a general general regret bound; a path length regret bound for a fixed smooth loss, applicable to an optimistic variant of regret-matching and regret-matching+; optimistic regret bounds  ...  The regret bounds attained for optimistic and adaptive Lagrangian hedging lead to a path length bound in constrained smooth convex optimization.  ... 
arXiv:2101.09603v2 fatcat:athlx5bagnd3dmbx5wl5mjfmie

Portfolio Optimization in Electricity Trading with Limited Liquidity

Oliver Woll, Christoph Weber
2007 Social Science Research Network  
used and the liquidity function assumed.  ...  Therefore the standard model has to be adapted to cope with limited liquidity.  ...  And in some cases the optimal hedging strategy involves overselling when using the empirical covariance matrix.  ... 
doi:10.2139/ssrn.1657014 fatcat:urj2jireqne6lovckl7suw5yui

Risk-Averse Model Predictive Control Design for Battery Energy Storage Systems

David Rosewater, Ross Baldick, Surya Santoso
2019 IEEE Transactions on Smart Grid  
To improve control performance and avoid optimistic shortfall, we develop a novel methodology for high performance, risk-averse battery energy storage controller design.  ...  susceptible to optimistic shortfall.  ...  ACKNOWLEDGMENT Sandia National Laboratories is a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International  ... 
doi:10.1109/tsg.2019.2946130 fatcat:ieki2drsenagnbkkl5nfo7jcrm

Decentralized Optimistic Hyperpolicy Mirror Descent: Provably No-Regret Learning in Markov Games [article]

Wenhao Zhan, Jason D. Lee, Zhuoran Yang
2022 arXiv   pre-print
The hyperpolicy is updated via mirror descent, where the update direction is obtained by an optimistic variant of least-squares policy evaluation.  ...  We study decentralized policy learning in Markov games where we control a single agent to play with nonstationary and possibly adversarial opponents.  ...  However, for an adaptive opponent, ν t will be chosen adaptively based on D 1:t−1 and we need to introduce an additional union bound over Π ′ when analyzing the evaluation error of V µ,ν t .  ... 
arXiv:2206.01588v1 fatcat:ocls5yclmvdbhfoo4ovsaezlqe

Minimax Optimal Quantile and Semi-Adversarial Regret via Root-Logarithmic Regularizers [article]

Jeffrey Negrea, Blair Bilodeau, Nicolò Campolongo, Francesco Orabona, Daniel M. Roy
2021 arXiv   pre-print
provide an adaptively minimax optimal algorithm for the semi-adversarial paradigm that adapts to the true, unknown constraint faster, leading to uniformly improved regret bounds over existing methods.  ...  Quantile (and, more generally, KL) regret bounds, such as those achieved by NormalHedge (Chaudhuri, Freund, and Hsu 2009) and its variants, relax the goal of competing against the best individual expert  ...  Acknowledgments and Disclosure of Funding JN is supported by an NSERC Vanier Canada Graduate Scholarship and the Vector Institute.  ... 
arXiv:2110.14804v2 fatcat:ubmpunh3lzdrnmtomvy4ndgvfa

Irrelevance of Short-Sale Constraints Under Ambiguity Aversion

Astrid V. Schornick
2006 Social Science Research Network  
Models of frictionless markets in which investors hold heterogeneous beliefs are observationally equivalent to those in which investors have di¤erent degrees of ambiguity aversion in the sense of Gilboa and  ...  Schmeidler (1989) : the investors who are more optimistic about a certain asset will hold more of it, just like ambiguity-averse investors will invest more in the stock that is less ambiguous to them.  ...  All the usual regularity conditions on drift and di¤usion parameters are assumed to hold, and all parameters are adapted to the …ltration generated by the agents'perceived Brownian Motions, according to  ... 
doi:10.2139/ssrn.676648 fatcat:vhs7l7xt3vg73a5q4l5ayhrce4

Monte Carlo bounding techniques for determining solution quality in stochastic programs

Wai-Kei Mak, David P. Morton, R.Kevin Wood
1999 Operations Research Letters  
We show that, in expectation, z * n is a lower bound on z * and that this bound monotonically improves as n increases.  ...  A sampling procedure based on common random numbers ensures nonnegative gap estimates and provides signiÿcant variance reduction over naive sampling on four test problems.  ...  Acknowledgements Swietanowski for access to their regularized decomposition code and thank the associate editor, David Goldsman, for many helpful comments.  ... 
doi:10.1016/s0167-6377(98)00054-6 fatcat:vtmywfzknngkzexromyqaivtgi

A stabilised scenario decomposition algorithm applied to stochastic unit commitment problems

Tim Schulze, Andreas Grothey, Ken McKinnon
2017 European Journal of Operational Research  
Takriti and Birge [5] apply the popular Progressive Hedging (PH) algorithm [18], which was developed for convex stochastic programs and can be used as a heuristic (without guarantee of convergence) in  ...  Individual units are linked by the load balance and spinning reserve constraints, and if those are relaxed, e.g. via Lagrangians [3] or augmented Lagrangians [14], the problem becomes separable by generators  ...  Acknowledgements We would like to thank the reviewers for their detailed comments and constructive suggestions which helped us to improve this paper.  ... 
doi:10.1016/j.ejor.2017.02.005 fatcat:wpyn6vt4ffar3jo4llogmqiz5a

Conic Blackwell Algorithm: Parameter-Free Convex-Concave Saddle-Point Solving [article]

Julien Grand-Clément, Christian Kroer
2021 arXiv   pre-print
We show how to implement CBA^+ for the simplex, ℓ_p norm balls, and ellipsoidal confidence regions in the simplex, and we present numerical experiments for solving matrix games and distributionally robust  ...  We develop new parameter-free and scale-free algorithms for solving convex-concave saddle-point problems.  ...  Note that a similar construction of a general class of algorithms can be achieved through the Lagrangian Hedging framework of Gordon [2007] .  ... 
arXiv:2105.13203v3 fatcat:fjv4z3mtlvgurph7fnqp5fknr4

A Fuzzy Prescriptive Analytics Approach to Power Generation Capacity Planning

Berna Tektaş, Hasan Hüseyin Turan, Nihat Kasap, Ferhan Çebi, Dursun Delen
2022 Energies  
Bellman and Zadeh's max-min criteria are used to transform the fuzzy capacity investment model into a model with a crisp objective and constraints.  ...  advanced combined-cycle natural gas, and steam (lignite) turbines.  ...  Game theory is engaged for almost all similar models, solved by stochastic dynamic programming [14] , Lagrangian relaxation and Benders decomposition [15, 16] evolutionary programming [17] Genetic  ... 
doi:10.3390/en15093176 fatcat:qmjtaxr6n5gbnj4dgdunk26e2e

Introduction to Multi-Armed Bandits [article]

Aleksandrs Slivkins
2022 arXiv   pre-print
The chapters on "bandits with similarity information", "bandits with knapsacks" and "bandits and agents" can also be consumed as standalone surveys on the respective topics.  ...  The appendix provides sufficient background on concentration and KL-divergence.  ...  , and choose the best arm based on these optimistic estimates.  ... 
arXiv:1904.07272v7 fatcat:pptyhyyshrdyhhf7bdonz5dsv4

Bounded gaps between primes in Chebotarev sets

Jesse Thorner
2014 Research in the Mathematical Sciences  
Learn about the classic results and their new developments. Infinitely many pairs of primes differ by no more than 70 million (and the bound's getting smaller every day)  ...  Flexible methods (known as Gromov's h-principle generalizing the work of Nash and Smale) played important role in symplectic topology from its inception.  ...  I Hedges, Global biogeochemical cycles: progress and problems, Marine Chemistry 39 (1992), 67-93. 32. J. I. Hedges and R. G.  ... 
doi:10.1186/2197-9847-1-4 fatcat:bybwtm5xyfbqrgmmm3dlbaumne

Electricity swing option pricing by stochastic bilevel optimization: A survey and new approaches

Raimund M. Kovacevic, Georg Ch. Pflug
2014 European Journal of Operational Research  
situations are analyzed: If the seller has strong market power he/she might be able to maximize his/her utility, while in fully competitive situations he/she will just look for a price which makes prot and  ...  In both cases the seller has to consider the decision problem of a potential buyer the valuation problem of determining a fair value for a specic option contract and anticipate the buyer's optimal reaction  ...  The largest part of the bilevel literature focuses on "optimistic" formulations in the style of (3.2) and we will follow this trend in the rest of this paper.  ... 
doi:10.1016/j.ejor.2013.12.029 fatcat:4rks2tnpc5fh5pveovymqtx7k4

Gamification of Pure Exploration for Linear Bandits [article]

Rémy Degenne, Pierre Ménard, Xuedong Shang, Michal Valko
2020 arXiv   pre-print
First, we provide a thorough comparison and new insight over different notions of optimality in the linear case, including G-optimality, transductive optimality from optimal experimental design and asymptotic  ...  Acknowledgements The research presented was supported by European CHIST-ERA project DELTA, French Ministry of Higher Education and Research, Nord-Pas-de-Calais Regional Council, and by French National  ...  Research Agency as part of the "Investissements d'avenir" program, reference ANR19-P3IA-0001 (PRAIRIE 3IA Institute) and the project BOLD, reference ANR19-CE23-0026-04.  ... 
arXiv:2007.00953v1 fatcat:fr5nptwpobgfdcyjhsotsi7yhu

Solving optimization problems with Blackwell approachability [article]

Julien Grand-Clément, Christian Kroer
2022 arXiv   pre-print
CBA^+ is based on Blackwell approachability and attains O(√(T)) regret.  ...  We introduce the Conic Blackwell Algorithm^+ (CBA^+) regret minimizer, a new parameter- and scale-free regret minimizer for general convex sets.  ...  While we use the framework of Abernethy et al. [2011] , we note that the Lagrangian Hedging framework of Gordon [2007] could also be used as the basis for developed a general class of Blackwell-approachability-style  ... 
arXiv:2202.12277v1 fatcat:vmp5ttavcra53nde5ojx7bzfem
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