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Register a new userExperiments with Game Tree Search in Real-Time Strategy Games
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Santiago Ontanon
Publication date
2012
fields
Informatics Engineering
and research's language is
English
Authors
Santiago Ontanon
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Game tree search algorithms such as minimax have been used with enormous success in turn-based adversarial games such as Chess or Checkers. However, such algorithms cannot be directly applied to real-time strategy (RTS) games because a number of reasons. For example, minimax assumes a turn-taking game mechanics, not present in RTS games. In this paper we present RTMM, a real-time variant of the standard minimax algorithm, and discuss its applicability in the context of RTS games. We discuss its strengths and weaknesses, and evaluate it in two real-time games.
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Games with large branching factors pose a significant challenge for game tree search algorithms. In this paper, we address this problem with a sampling strategy for Monte Carlo Tree Search (MCTS) algorithms called {em na{i}ve sampling}, based on a variant of the Multi-armed Bandit problem called {em Combinatorial Multi-armed Bandits} (CMAB). We analyze the theoretical properties of several variants of {em na{i}ve sampling}, and empirically compare it against the other existing strategies in the literature for CMABs. We then evaluate these strategies in the context of real-time strategy (RTS) games, a genre of computer games characterized by their very large branching factors. Our results show that as the branching factor grows, {em na{i}ve sampling} outperforms the other sampling strategies.
We study an information-structure design problem (a.k.a. persuasion) with a single sender and multiple receivers with actions of a priori unknown types, independently drawn from action-specific marginal distributions. As in the standard Bayesian persuasion model, the sender has access to additional information regarding the action types, which she can exploit when committing to a (noisy) signaling scheme through which she sends a private signal to each receiver. The novelty of our model is in considering the case where the receivers interact in a sequential game with imperfect information, with utilities depending on the game outcome and the realized action types. After formalizing the notions of ex ante and ex interim persuasiveness (which differ in the time at which the receivers commit to following the senders signaling scheme), we investigate the continuous optimization problem of computing a signaling scheme which maximizes the senders expected revenue. We show that computing an optimal ex ante persuasive signaling scheme is NP-hard when there are three or more receivers. In contrast with previous hardness results for ex interim persuasion, we show that, for games with two receivers, an optimal ex ante persuasive signaling scheme can be computed in polynomial time thanks to a novel algorithm based on the ellipsoid method which we propose.
Bid optimization for online advertising from single advertisers perspective has been thoroughly investigated in both academic research and industrial practice. However, existing work typically assume competitors do not change their bids, i.e., the wining price is fixed, leading to poor performance of the derived solution. Although a few studies use multi-agent reinforcement learning to set up a cooperative game, they still suffer the following drawbacks: (1) They fail to avoid collusion solutions where all the advertisers involved in an auction collude to bid an extremely low price on purpose. (2) Previous works cannot well handle the underlying complex bidding environment, leading to poor model convergence. This problem could be amplified when handling multiple objectives of advertisers which are practical demands but not considered by previous work. In this paper, we propose a novel multi-objective cooperative bid optimization formulation called Multi-Agent Cooperative bidding Games (MACG). MACG sets up a carefully designed multi-objective optimization framework where different objectives of advertisers are incorporated. A global objective to maximize the overall profit of all advertisements is added in order to encourage better cooperation and also to protect self-bidding advertisers. To avoid collusion, we also introduce an extra platform revenue constraint. We analyze the optimal functional form of the bidding formula theoretically and design a policy network accordingly to generate auction-level bids. Then we design an efficient multi-agent evolutionary strategy for model optimization. Offline experiments and online A/B tests conducted on the Taobao platform indicate both single advertisers objective and global profit have been significantly improved compared to state-of-art methods.
Hero drafting is essential in MOBA game playing as it builds the team of each side and directly affects the match outcome. State-of-the-art drafting methods fail to consider: 1) drafting efficiency when the hero pool is expanded; 2) the multi-round nature of a MOBA 5v5 match series, i.e., two teams play best-of-N and the same hero is only allowed to be drafted once throughout the series. In this paper, we formulate the drafting process as a multi-round combinatorial game and propose a novel drafting algorithm based on neural networks and Monte-Carlo tree search, named JueWuDraft. Specifically, we design a long-term value estimation mechanism to handle the best-of-N drafting case. Taking Honor of Kings, one of the most popular MOBA games at present, as a running case, we demonstrate the practicality and effectiveness of JueWuDraft when compared to state-of-the-art drafting methods.
We focus on adversarial patrolling games on arbitrary graphs, where the Defender can control a mobile resource, the targets are alarmed by an alarm system, and the Attacker can observe the actions of the mobile resource of the Defender and perform different attacks exploiting multiple resources. This scenario can be modeled as a zero-sum extensive-form game in which each player can play multiple times. The game tree is exponentially large both in the size of the graph and in the number of attacking resources. We show that when the number of the Attackers resources is free, the problem of computing the equilibrium path is NP-hard, while when the number of resources is fixed, the equilibrium path can be computed in poly-time. We provide a dynamic-programming algorithm that, given the number of the Attackers resources, computes the equilibrium path requiring poly-time in the size of the graph and exponential time in the number of the resources. Furthermore, since in real-world scenarios it is implausible that the Defender knows the number of attacking resources, we study the robustness of the Defenders strategy when she makes a wrong guess about that number. We show that even the error of just a single resource can lead to an arbitrary inefficiency, when the inefficiency is defined as the ratio of the Defenders utilities obtained with a wrong guess and a correct guess. However, a more suitable definition of inefficiency is given by the difference of the Defenders utilities: this way, we observe that the higher the error in the estimation, the higher the loss for the Defender. Then, we investigate the performance of online algorithms when no information about the Attackers resources is available. Finally, we resort to randomized online algorithms showing that we can obtain a competitive factor that is twice better than the one that can be achieved by any deterministic online algorithm.
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