Martin Müller

Timo Bertram, Johannes Fürnkranz, Martin Müller

A defining feature of collectable card games is the deck building process prior to actual gameplay, in which players form their decks according to some restrictions. Learning to build decks is difficult for players and models alike due to the large card variety and highly complex semantics, as well as requiring meaningful card and deck representations when aiming to utilise AI. In addition, regular releases of new card sets lead to unforeseeable fluctuations in the available card pool, thus affecting possible deck configurations and requiring continuous updates. Previous Game AI approaches to building decks have often been limited to fixed sets of possible cards, which greatly limits their utility in practice. In this work, we explore possible card representations that generalise to unseen cards, thus greatly extending the real-world utility of AI-based deck building for the game "Magic: The Gathering".We study such representations based on numerical, nominal, and text-based features of cards, card images, and meta information about card usage from third-party services. Our results show that while the particular choice of generalised input representation has little effect on learning to predict human card selections among known cards, the performance on new, unseen cards can be greatly improved. Our generalised model is able to predict 55\% of human choices on completely unseen cards, thus showing a deep understanding of card quality and strategy.

Timo Bertram, Johannes Fürnkranz, Martin Müller

In imperfect information games, the game state is generally not fully observable to players. Therefore, good gameplay requires policies that deal with the different information that is hidden from each player. To combat this, effective algorithms often reason about information sets; the sets of all possible game states that are consistent with a player's observations. While there is no way to distinguish between the states within an information set, this property does not imply that all states are equally likely to occur in play. We extend previous research on assigning weights to the states in an information set in order to facilitate better gameplay in the imperfect information game of Reconnaissance Blind Chess. For this, we train two different neural networks which estimate the likelihood of each state in an information set from historical game data. Experimentally, we find that a Siamese neural network is able to achieve higher accuracy and is more efficient than a classical convolutional neural network for the given domain. Finally, we evaluate an RBC-playing agent that is based on the generated weightings and compare different parameter settings that influence how strongly it should rely on them. The resulting best player is ranked 5th on the public leaderboard.

Timo Bertram, Johannes Fürnkranz, Martin Müller

In imperfect information games, the evaluation of a game state not only depends on the observable world but also relies on hidden parts of the environment. As accessing the obstructed information trivialises state evaluations, one approach to tackle such problems is to estimate the value of the imperfect state as a combination of all states in the information set, i.e., all possible states that are consistent with the current imperfect information. In this work, the goal is to learn a function that maps from the imperfect game information state to its expected value. However, constructing a perfect training set, i.e. an enumeration of the whole information set for numerous imperfect states, is often infeasible. To compute the expected values for an imperfect information game like \textit{Reconnaissance Blind Chess}, one would need to evaluate thousands of chess positions just to obtain the training target for a single state. Still, the expected value of a state can already be approximated with appropriate accuracy from a much smaller set of evaluations. Thus, in this paper, we empirically investigate how a budget of perfect information game evaluations should be distributed among training samples to maximise the return. Our results show that sampling a small number of states, in our experiments roughly 3, for a larger number of separate positions is preferable over repeatedly sampling a smaller quantity of states. Thus, we find that in our case, the quantity of different samples seems to be more important than higher target quality.

Hongming Zhang, Fengshuo Bai, Chenjun Xiao et al.

While many sophisticated exploration methods have been proposed, their lack of generality and high computational cost often lead researchers to favor simpler methods like $ε$-greedy. Motivated by this, we introduce $β$-DQN, a simple and efficient exploration method that augments the standard DQN with a behavior function $β$. This function estimates the probability that each action has been taken at each state. By leveraging $β$, we generate a population of diverse policies that balance exploration between state-action coverage and overestimation bias correction. An adaptive meta-controller is designed to select an effective policy for each episode, enabling flexible and explainable exploration. $β$-DQN is straightforward to implement and adds minimal computational overhead to the standard DQN. Experiments on both simple and challenging exploration domains show that $β$-DQN outperforms existing baseline methods across a wide range of tasks, providing an effective solution for improving exploration in deep reinforcement learning.

Farnaz Kohankhaki, Kiarash Aghakasiri, Hongming Zhang et al.

Monte Carlo Tree Search (MCTS) is an immensely popular search-based framework used for decision making. It is traditionally applied to domains where a perfect simulation model of the environment is available. We study and improve MCTS in the context where the environment model is given but imperfect. We show that the discrepancy between the model and the actual environment can lead to significant performance degradation with standard MCTS. We therefore develop Uncertainty Adapted MCTS (UA-MCTS), a more robust algorithm within the MCTS framework. We estimate the transition uncertainty in the given model, and direct the search towards more certain transitions in the state space. We modify all four MCTS phases to improve the search behavior by considering these estimates. We prove, in the corrupted bandit case, that adding uncertainty information to adapt UCB leads to tighter regret bound than standard UCB. Empirically, we evaluate UA-MCTS and its individual components on the deterministic domains from the MinAtar test suite. Our results demonstrate that UA-MCTS strongly improves MCTS in the presence of model transition errors.

Yue Pei, Hongming Zhang, Chao Gao et al.

Offline reinforcement learning (RL) has achieved significant advances in domains such as robotic control, autonomous driving, and medical decision-making. Most existing methods primarily focus on training policies that maximize cumulative returns from a given dataset. However, many real-world applications require precise control over policy performance levels, rather than simply pursuing the best possible return. Reinforcement learning via supervised learning (RvS) frames offline RL as a sequence modeling task, enabling the extraction of diverse policies by conditioning on different desired returns. Yet, existing RvS-based transformers, such as Decision Transformer (DT), struggle to reliably align the actual achieved returns with specified target returns, especially when interpolating within underrepresented returns or extrapolating beyond the dataset. To address this limitation, we propose Doctor, a novel approach that Double Checks the Transformer with target alignment for Offline RL. Doctor integrates the strengths of supervised learning (SL) and temporal difference (TD) learning by jointly optimizing the action prediction and value estimation. During inference, Doctor introduces a double-check mechanism: actions are first sampled around the desired target returns and then validated with value functions. This ensures more accurate alignment between predicted actions and desired target returns. We evaluate Doctor on the D4RL and EpiCare benchmarks, demonstrating aligned control yields stronger performance and tunable expertise, showing its effectiveness in a wide range of tasks.

Owen Randall, Martin Müller, Ting Han Wei et al.

We propose Expected Work Search (EWS), a new game solving algorithm. EWS combines win rate estimation, as used in Monte Carlo Tree Search, with proof size estimation, as used in Proof Number Search. The search efficiency of EWS stems from minimizing a novel notion of Expected Work, which predicts the expected computation required to solve a position. EWS outperforms traditional solving algorithms on the games of Go and Hex. For Go, we present the first solution to the empty 5x5 board with the commonly used positional superko ruleset. For Hex, our algorithm solves the empty 8x8 board in under 4 minutes. Experiments show that EWS succeeds both with and without extensive domain-specific knowledge.

Hongming Zhang, Ke Sun, Bo Xu et al.

In deep reinforcement learning (RL) systems, abnormal states pose significant risks by potentially triggering unpredictable behaviors and unsafe actions, thus impeding the deployment of RL systems in real-world scenarios. It is crucial for reliable decision-making systems to have the capability to cast an alert whenever they encounter unfamiliar observations that they are not equipped to handle. In this paper, we propose a novel Mahalanobis distance-based (MD) anomaly detection framework, called \textit{MDX}, for deep RL algorithms. MDX simultaneously addresses random, adversarial, and out-of-distribution (OOD) state outliers in both offline and online settings. It utilizes Mahalanobis distance within class-conditional distributions for each action and operates within a statistical hypothesis testing framework under the Gaussian assumption. We further extend it to robust and distribution-free versions by incorporating Robust MD and conformal inference techniques. Through extensive experiments on classical control environments, Atari games, and autonomous driving scenarios, we demonstrate the effectiveness of our MD-based detection framework. MDX offers a simple, unified, and practical anomaly detection tool for enhancing the safety and reliability of RL systems in real-world applications.

Timo Bertram, Johannes Fürnkranz, Martin Müller

In this paper, we study the problem of evaluating the addition of elements to a set. This problem is difficult, because it can, in the general case, not be reduced to unconditional preferences between the choices. Therefore, we model preferences based on the context of the decision. We discuss and compare two different Siamese network architectures for this task: a twin network that compares the two sets resulting after the addition, and a triplet network that models the contribution of each candidate to the existing set. We evaluate the two settings on a real-world task; learning human card preferences for deck building in the collectible card game Magic: The Gathering. We show that the triplet approach achieves a better result than the twin network and that both outperform previous results on this task.

Chenjun Xiao, Yifan Wu, Chen Ma et al.

Despite its potential to improve sample complexity versus model-free approaches, model-based reinforcement learning can fail catastrophically if the model is inaccurate. An algorithm should ideally be able to trust an imperfect model over a reasonably long planning horizon, and only rely on model-free updates when the model errors get infeasibly large. In this paper, we investigate techniques for choosing the planning horizon on a state-dependent basis, where a state's planning horizon is determined by the maximum cumulative model error around that state. We demonstrate that these state-dependent model errors can be learned with Temporal Difference methods, based on a novel approach of temporally decomposing the cumulative model errors. Experimental results show that the proposed method can successfully adapt the planning horizon to account for state-dependent model accuracy, significantly improving the efficiency of policy learning compared to model-based and model-free baselines.

Ruitong Huang, Mohammad M. Ajallooeian, Csaba Szepesvári et al.

We study the problem of identifying the best action among a set of possible options when the value of each action is given by a mapping from a number of noisy micro-observables in the so-called fixed confidence setting. Our main motivation is the application to the minimax game search, which has been a major topic of interest in artificial intelligence. In this paper we introduce an abstract setting to clearly describe the essential properties of the problem. While previous work only considered a two-move game tree search problem, our abstract setting can be applied to the general minimax games where the depth can be non-uniform and arbitrary, and transpositions are allowed. We introduce a new algorithm (LUCB-micro) for the abstract setting, and give its lower and upper sample complexity results. Our bounds recover some previous results, which were only available in more limited settings, while they also shed further light on how the structure of minimax problems influence sample complexity.