Related papers: Artificial intelligence for Bidding Hex

In the field of Artificial Intelligence, traditional approaches to choosing moves in games involve the we of the minimax algorithm. However, recent research results indicate that minimizing may not always be the best approach. In this paper…

This paper develops a new dual approach to compute the hedging portfolio of a Bermudan option and its initial value. It gives a "purely dual" algorithm following the spirit of Rogers (2010) in the sense that it only relies on the dual…

We describe the probability theory behind a casino game, blackjack, and the procedure to compute the optimal strategy for a deck of arbitrary cards and player's expected win given that he follows the optimal strategy. The exact blackjack…

Three possibilities to speed up the Hybrid Monte Carlo algorithm are investigated. Changing the step-size adaptively brings no practical gain. On the other hand, substantial improvements result from using an approximate Hamiltonian or a…

Bidding chess is a chess variant where instead of alternating play, players bid for the opportunity to move. Generalizing a known result on so-called Richman games, we show that for a natural class of games including bidding chess, each…

In a multiple-object auction, every bidder tries to win as many objects as possible with a bidding algorithm. This paper studies position-randomized auctions, which form a special class of multiple-object auctions where a bidding algorithm…

In this article, we introduce an algorithm called Backward Hedging, designed for hedging European and American options while considering transaction costs. The optimal strategy is determined by minimizing an appropriate loss function, which…

We consider random-turn positional games, introduced by Peres, Schramm, Sheffield and Wilson in 2007. A $p$-random-turn positional game is a two-player game, played the same as an ordinary positional game, except that instead of alternating…

In this paper we present two parallel Monte Carlo based algorithms for pricing multi--dimensional Bermudan/American options. First approach relies on computation of the optimal exercise boundary while the second relies on classification of…

By analogy with Monte Carlo algorithms, we propose new strategies for design and redesign of small molecule libraries in high-throughput experimentation, or combinatorial chemistry. Several Monte Carlo methods are examined, including…

Monte Carlo Tree Search (MCTS), most famously used in game-play artificial intelligence (e.g., the game of Go), is a well-known strategy for constructing approximate solutions to sequential decision problems. Its primary innovation is the…

We will try to tackle both the theoretical and practical aspects of a very important problem in chess programming as stated in the title of this article - the issue of draw detection by move repetition. The standard approach that has so far…

Recent advances in bandit tools and techniques for sequential learning are steadily enabling new applications and are promising the resolution of a range of challenging related problems. We study the game tree search problem, where the goal…

Adversarial training, a special case of multi-objective optimization, is an increasingly prevalent machine learning technique: some of its most notable applications include GAN-based generative modeling and self-play techniques in…

Hex is a complex game with a high branching factor. For the first time Hex is being attempted to be solved without the use of game tree structures and associated methods of pruning. We also are abstaining from any heuristic information…

Hex is a turn-based two-player connection game with a high branching factor, making the game arbitrarily complex with increasing board sizes. As such, top-performing algorithms for playing Hex rely on accurate evaluation of board positions…

Recent advances in machine learning have spurred significant interest in learning-augmented algorithms, particularly for online optimization. A growing body of work has studied online bidding in this framework, aiming to characterize the…

Mastering the game of Go has remained a long standing challenge to the field of AI. Modern computer Go systems rely on processing millions of possible future positions to play well, but intuitively a stronger and more 'humanlike' way to…

We study the basic allocation problem of assigning resources to players so as to maximize fairness. This is one of the few natural problems that enjoys the intriguing status of having a better estimation algorithm than approximation…

Building on the work of Schweizer (1995) and Cern and Kallseny (2007), we present discrete time formulas minimizing the mean square hedging error for multidimensional assets. In particular, we give explicit formulas when a regime-switching…