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Nick Petosa
Publication date
2019
fields
Informatics Engineering
and research's language is
English
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The AlphaZero algorithm has achieved superhuman performance in two-player, deterministic, zero-sum games where perfect information of the game state is available. This success has been demonstrated in Chess, Shogi, and Go where learning occurs solely through self-play. Many real-world applications (e.g., equity trading) require the consideration of a multiplayer environment. In this work, we suggest novel modifications of the AlphaZero algorithm to support multiplayer environments, and evaluate the approach in two simple 3-player games. Our experiments show that multiplayer AlphaZero learns successfully and consistently outperforms a competing approach: Monte Carlo tree search. These results suggest that our modified AlphaZero can learn effective strategies in multiplayer game scenarios. Our work supports the use of AlphaZero in multiplayer games and suggests future research for more complex environments.
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Morpion Solitaire is a popular single player game, performed with paper and pencil. Due to its large state space (on the order of the game of Go) traditional search algorithms, such as MCTS, have not been able to find good solutions. A later algorithm, Nested Rollout Policy Adaptation, was able to find a new record of 82 steps, albeit with large computational resources. After achieving this record, to the best of our knowledge, there has been no further progress reported, for about a decade. In this paper we take the recent impressive performance of deep self-learning reinforcement learning approaches from AlphaGo/AlphaZero as inspiration to design a searcher for Morpion Solitaire. A challenge of Morpion Solitaire is that the state space is sparse, there are few win/loss signals. Instead, we use an approach known as ranked reward to create a reinforcement learning self-play framework for Morpion Solitaire. This enables us to find medium-quality solutions with reasonable computational effort. Our record is a 67 steps solution, which is very close to the human best (68) without any other adaptation to the problem than using ranked reward. We list many further avenues for potential improvement.
Multiplayer games have long been used as testbeds in artificial intelligence research, aptly referred to as the Drosophila of artificial intelligence. Traditionally, researchers have focused on using well-known games to build strong agents. This progress, however, can be better informed by characterizing games and their topological landscape. Tackling this latter question can facilitate understanding of agents and help determine what game an agent should target next as part of its training. Here, we show how network measures applied to response graphs of large-scale games enable the creation of a landscape of games, quantifying relationships between games of varying sizes and characteristics. We illustrate our findings in domains ranging from canonical games to complex empirical games capturing the performance of trained agents pitted against one another. Our results culminate in a demonstration leveraging this information to generate new and interesting games, including mixtures of empirical games synthesized from real world games.
Multiplayer Online Battle Arena (MOBA) games have received increasing popularity recently. In a match of such games, players compete in two teams of five, each controlling an in-game avatars, known as heroes, selected from a roster of more than 100. The selection of heroes, also known as pick or draft, takes place before the match starts and alternates between the two teams until each player has selected one hero. Heroes are designed with different strengths and weaknesses to promote team cooperation in a game. Intuitively, heroes in a strong team should complement each others strengths and suppressing those of opponents. Hero drafting is therefore a challenging problem due to the complex hero-to-hero relationships to consider. In this paper, we propose a novel hero recommendation system that suggests heroes to add to an existing team while maximizing the teams prospect for victory. To that end, we model the drafting between two teams as a combinatorial game and use Monte Carlo Tree Search (MCTS) for estimating the values of hero combinations. Our empirical evaluation shows that hero teams drafted by our recommendation algorithm have significantly higher win rate against teams constructed by other baseline and state-of-the-art strategies.
We investigate the value of parallel repetition of one-round games with any number of players $kge 2$. It has been an open question whether an analogue of Razs Parallel Repetition Theorem holds for games with more than two players, i.e., whether the value of the repeated game decays exponentially with the number of repetitions. Verbitsky has shown, via a reduction to the density Hales-Jewett theorem, that the value of the repeated game must approach zero, as the number of repetitions increases. However, the rate of decay obtained in this way is extremely slow, and it is an open question whether the true rate is exponential as is the case for all two-player games. Exponential decay bounds are known for several special cases of multi-player games, e.g., free games and anchored games. In this work, we identify a certain expansion property of the base game and show all games with this property satisfy an exponential decay parallel repetition bound. Free games and anchored games satisfy this expansion property, and thus our parallel repetition theorem reproduces all earlier exponential-decay bounds for multiplayer games. More generally, our parallel repetition bound applies to all multiplayer games that are connected in a certain sense. We also describe a very simple game, called the GHZ game, that does not satisfy this connectivity property, and for which we do not know an exponential decay bound. We suspect that progress on bounding the value of this the parallel repetition of the GHZ game will lead to further progress on the general question.
Successful analysis of player skills in video games has important impacts on the process of enhancing player experience without undermining their continuous skill development. Moreover, player skill analysis becomes more intriguing in team-based video games because such form of study can help discover useful factors in effective team formation. In this paper, we consider the problem of skill decomposition in MOBA (MultiPlayer Online Battle Arena) games, with the goal to understand what player skill factors are essential for the outcome of a game match. To understand the construct of MOBA player skills, we utilize various skill-based predictive models to decompose player skills into interpretative parts, the impact of which are assessed in statistical terms. We apply this analysis approach on two widely known MOBAs, namely League of Legends (LoL) and Defense of the Ancients 2 (DOTA2). The finding is that base skills of in-game avatars, base skills of players, and players champion-specific skills are three prominent skill components influencing LoLs match outcomes, while those of DOTA2 are mainly impacted by in-game avatars base skills but not much by the other two.
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