Martin Schmid

Radovan Haluska, Martin Schmid

While Poker, as a family of games, has been studied extensively in the last decades, collectible card games have seen relatively little attention. Only recently have we seen an agent that can compete with professional human players in Hearthstone, one of the most popular collectible card games. Although artificial agents must be able to work with imperfect information in both of these genres, collectible card games pose another set of distinct challenges. Unlike in many poker variants, agents must deal with state space so vast that even enumerating all states consistent with the agent's beliefs is intractable, rendering the current search methods unusable and requiring the agents to opt for other techniques. In this paper, we investigate the strength of such techniques for this class of games. Namely, we present preliminary analysis results of ByteRL, the state-of-the-art agent in Legends of Code and Magic and Hearthstone. Although ByteRL beat a top-10 Hearthstone player from China, we show that its play in Legends of Code and Magic is highly exploitable.

Martin Schmid

From the very dawn of the field, search with value functions was a fundamental concept of computer games research. Turing's chess algorithm from 1950 was able to think two moves ahead, and Shannon's work on chess from $1950$ includes an extensive section on evaluation functions to be used within a search. Samuel's checkers program from 1959 already combines search and value functions that are learned through self-play and bootstrapping. TD-Gammon improves upon those ideas and uses neural networks to learn those complex value functions -- only to be again used within search. The combination of decision-time search and value functions has been present in the remarkable milestones where computers bested their human counterparts in long standing challenging games -- DeepBlue for Chess and AlphaGo for Go. Until recently, this powerful framework of search aided with (learned) value functions has been limited to perfect information games. As many interesting problems do not provide the agent perfect information of the environment, this was an unfortunate limitation. This thesis introduces the reader to sound search for imperfect information games.

Audrūnas Gruslys, Marc Lanctot, Rémi Munos et al.

Regret minimization has played a key role in online learning, equilibrium computation in games, and reinforcement learning (RL). In this paper, we describe a general model-free RL method for no-regret learning based on repeated reconsideration of past behavior. We propose a model-free RL algorithm, the AdvantageRegret-Matching Actor-Critic (ARMAC): rather than saving past state-action data, ARMAC saves a buffer of past policies, replaying through them to reconstruct hindsight assessments of past behavior. These retrospective value estimates are used to predict conditional advantages which, combined with regret matching, produces a new policy. In particular, ARMAC learns from sampled trajectories in a centralized training setting, without requiring the application of importance sampling commonly used in Monte Carlo counterfactual regret (CFR) minimization; hence, it does not suffer from excessive variance in large environments. In the single-agent setting, ARMAC shows an interesting form of exploration by keeping past policies intact. In the multiagent setting, ARMAC in self-play approaches Nash equilibria on some partially-observable zero-sum benchmarks. We provide exploitability estimates in the significantly larger game of betting-abstracted no-limit Texas Hold'em.

Finbarr Timbers, Nolan Bard, Edward Lockhart et al.

Researchers have demonstrated that neural networks are vulnerable to adversarial examples and subtle environment changes, both of which one can view as a form of distribution shift. To humans, the resulting errors can look like blunders, eroding trust in these agents. In prior games research, agent evaluation often focused on the in-practice game outcomes. While valuable, such evaluation typically fails to evaluate robustness to worst-case outcomes. Prior research in computer poker has examined how to assess such worst-case performance, both exactly and approximately. Unfortunately, exact computation is infeasible with larger domains, and existing approximations rely on poker-specific knowledge. We introduce ISMCTS-BR, a scalable search-based deep reinforcement learning algorithm for learning a best response to an agent, thereby approximating worst-case performance. We demonstrate the technique in several two-player zero-sum games against a variety of agents, including several AlphaZero-based agents.

Trevor Davis, Martin Schmid, Michael Bowling

Extensive-form games (EFGs) are a common model of multi-agent interactions with imperfect information. State-of-the-art algorithms for solving these games typically perform full walks of the game tree that can prove prohibitively slow in large games. Alternatively, sampling-based methods such as Monte Carlo Counterfactual Regret Minimization walk one or more trajectories through the tree, touching only a fraction of the nodes on each iteration, at the expense of requiring more iterations to converge due to the variance of sampled values. In this paper, we extend recent work that uses baseline estimates to reduce this variance. We introduce a framework of baseline-corrected values in EFGs that generalizes the previous work. Within our framework, we propose new baseline functions that result in significantly reduced variance compared to existing techniques. We show that one particular choice of such a function --- predictive baseline --- is provably optimal under certain sampling schemes. This allows for efficient computation of zero-variance value estimates even along sampled trajectories.

Martin Schmid, Neil Burch, Marc Lanctot et al.

Learning strategies for imperfect information games from samples of interaction is a challenging problem. A common method for this setting, Monte Carlo Counterfactual Regret Minimization (MCCFR), can have slow long-term convergence rates due to high variance. In this paper, we introduce a variance reduction technique (VR-MCCFR) that applies to any sampling variant of MCCFR. Using this technique, per-iteration estimated values and updates are reformulated as a function of sampled values and state-action baselines, similar to their use in policy gradient reinforcement learning. The new formulation allows estimates to be bootstrapped from other estimates within the same episode, propagating the benefits of baselines along the sampled trajectory; the estimates remain unbiased even when bootstrapping from other estimates. Finally, we show that given a perfect baseline, the variance of the value estimates can be reduced to zero. Experimental evaluation shows that VR-MCCFR brings an order of magnitude speedup, while the empirical variance decreases by three orders of magnitude. The decreased variance allows for the first time CFR+ to be used with sampling, increasing the speedup to two orders of magnitude.

Matej Moravčík, Martin Schmid, Neil Burch et al.

Artificial intelligence has seen several breakthroughs in recent years, with games often serving as milestones. A common feature of these games is that players have perfect information. Poker is the quintessential game of imperfect information, and a longstanding challenge problem in artificial intelligence. We introduce DeepStack, an algorithm for imperfect information settings. It combines recursive reasoning to handle information asymmetry, decomposition to focus computation on the relevant decision, and a form of intuition that is automatically learned from self-play using deep learning. In a study involving 44,000 hands of poker, DeepStack defeated with statistical significance professional poker players in heads-up no-limit Texas hold'em. The approach is theoretically sound and is shown to produce more difficult to exploit strategies than prior approaches.

Neil Burch, Martin Schmid, Matej Moravčík et al.

Evaluating agent performance when outcomes are stochastic and agents use randomized strategies can be challenging when there is limited data available. The variance of sampled outcomes may make the simple approach of Monte Carlo sampling inadequate. This is the case for agents playing heads-up no-limit Texas hold'em poker, where man-machine competitions have involved multiple days of consistent play and still not resulted in statistically significant conclusions even when the winner's margin is substantial. In this paper, we introduce AIVAT, a low variance, provably unbiased value assessment tool that uses an arbitrary heuristic estimate of state value, as well as the explicit strategy of a subset of the agents. Unlike existing techniques which reduce the variance from chance events, or only consider game ending actions, AIVAT reduces the variance both from choices by nature and by players with a known strategy. The resulting estimator in no-limit poker can reduce the number of hands needed to draw statistical conclusions by more than a factor of 10.

Rudolf Kadlec, Martin Schmid, Ondrej Bajgar et al.

Several large cloze-style context-question-answer datasets have been introduced recently: the CNN and Daily Mail news data and the Children's Book Test. Thanks to the size of these datasets, the associated text comprehension task is well suited for deep-learning techniques that currently seem to outperform all alternative approaches. We present a new, simple model that uses attention to directly pick the answer from the context as opposed to computing the answer using a blended representation of words in the document as is usual in similar models. This makes the model particularly suitable for question-answering problems where the answer is a single word from the document. Ensemble of our models sets new state of the art on all evaluated datasets.

Rudolf Kadlec, Martin Schmid, Jan Kleindienst

This paper presents results of our experiments for the next utterance ranking on the Ubuntu Dialog Corpus -- the largest publicly available multi-turn dialog corpus. First, we use an in-house implementation of previously reported models to do an independent evaluation using the same data. Second, we evaluate the performances of various LSTMs, Bi-LSTMs and CNNs on the dataset. Third, we create an ensemble by averaging predictions of multiple models. The ensemble further improves the performance and it achieves a state-of-the-art result for the next utterance ranking on this dataset. Finally, we discuss our future plans using this corpus.