arXiv subjects

James R. Wright

Publications and source records attributed to James R. Wright.

23 records · Page 2Linked to original sources

arXiv2019

Bounds for Approximate Regret-Matching Algorithms

A dominant approach to solving large imperfect-information games is Counterfactural Regret Minimization (CFR). In CFR, many regret minimization problems are combined to solve the game. For very large games, abstraction is typically needed to render CFR tractable. Abstractions are often manually tuned, possibly removing important strategic differences in the full game and harming performance. Function approximation provides a natural solution to finding good abstractions to approximate the full game. A common approach to incorporating function approximation is to learn the inputs needed for a regret minimizing algorithm, allowing for generalization across many regret minimization problems. This paper gives regret bounds when a regret minimizing algorithm uses estimates instead of true values. This form of analysis is the first to generalize to a larger class of $(Φ, f)$-regret matching algorithms, and includes different forms of regret such as swap, internal, and external regret. We demonstrate how these results give a slightly tighter bound for Regression Regret-Matching (RRM), and present a novel bound for combining regression with Hedge.

cs.LG↗

arXiv2017

Learning in the Repeated Secretary Problem

In the classical secretary problem, one attempts to find the maximum of an unknown and unlearnable distribution through sequential search. In many real-world searches, however, distributions are not entirely unknown and can be learned through experience. To investigate learning in such a repeated secretary problem we conduct a large-scale behavioral experiment in which people search repeatedly from fixed distributions. In contrast to prior investigations that find no evidence for learning in the classical scenario, in the repeated setting we observe substantial learning resulting in near-optimal stopping behavior. We conduct a Bayesian comparison of multiple behavioral models which shows that participants' behavior is best described by a class of threshold-based models that contains the theoretically optimal strategy. Fitting such a threshold-based model to data reveals players' estimated thresholds to be surprisingly close to the optimal thresholds after only a small number of games.

cs.GT↗

arXiv2017

Predicting Human Behavior in Unrepeated, Simultaneous-Move Games

It is common to assume that agents will adopt Nash equilibrium strategies; however, experimental studies have demonstrated that Nash equilibrium is often a poor description of human players' behavior in unrepeated normal-form games. In this paper, we analyze five widely studied models (Quantal Response Equilibrium, Level-k, Cognitive Hierarchy, QLk, and Noisy Introspection) that aim to describe actual, rather than idealized, human behavior in such games. We performed what we believe is the most comprehensive meta-analysis of these models, leveraging ten different data sets from the literature recording human play of two-player games. We began by evaluating the models' generalization or predictive performance, asking how well a model fits unseen test data after having had its parameters calibrated based on separate training data. Surprisingly, we found that what we dub the QLk model of Stahl & Wilson (1994) consistently achieved the best performance. Motivated by this finding, we describe methods for analyzing the posterior distributions over a model's parameters. We found that QLk's parameters were being set to values that were not consistent with their intended economic interpretations. We thus explored variations of QLk, ultimately identifying a new model family that has fewer parameters, gives rise to more parsimonious parameter values, and achieves better predictive performance.

cs.GT↗

arXiv2016

Models of Level-0 Behavior for Predicting Human Behavior in Games

Behavioral game theory seeks to describe the way actual people (as compared to idealized, "rational" agents) act in strategic situations. Our own recent work has identified iterative models (such as quantal cognitive hierarchy) as the state of the art for predicting human play in unrepeated, simultaneous-move games (Wright & Leyton-Brown 2012, 2016). Iterative models predict that agents reason iteratively about their opponents, building up from a specification of nonstrategic behavior called level-0. The modeler is in principle free to choose any description of level-0 behavior that makes sense for the setting. However, almost all existing work specifies this behavior as a uniform distribution over actions. In most games it is not plausible that even nonstrategic agents would choose an action uniformly at random, nor that other agents would expect them to do so. A more accurate model for level-0 behavior has the potential to dramatically improve predictions of human behavior, since a substantial fraction of agents may play level-0 strategies directly, and furthermore since iterative models ground all higher-level strategies in responses to the level-0 strategy. Our work considers models of the way in which level-0 agents construct a probability distribution over actions, given an arbitrary game. Using a Bayesian optimization package called SMAC (Hutter, Hoos, & Leyton-Brown, 2010, 2011, 2012), we systematically evaluated a large space of such models, each of which makes its prediction based only on general features that can be computed from any normal form game. In the end, we recommend a model that achieved excellent performance across the board: a linear weighting of features that requires the estimation of four weights. We evaluated the effects of combining this new level-0 model with several iterative models, and observed large improvements in the models' predictive accuracies.

cs.GT↗

arXiv2016

Incentivizing Evaluation via Limited Access to Ground Truth: Peer-Prediction Makes Things Worse

In many settings, an effective way of evaluating objects of interest is to collect evaluations from dispersed individuals and to aggregate these evaluations together. Some examples are categorizing online content and evaluating student assignments via peer grading. For this data science problem, one challenge is to motivate participants to conduct such evaluations carefully and to report them honestly, particularly when doing so is costly. Existing approaches, notably peer-prediction mechanisms, can incentivize truth telling in equilibrium. However, they also give rise to equilibria in which agents do not pay the costs required to evaluate accurately, and hence fail to elicit useful information. We show that this problem is unavoidable whenever agents are able to coordinate using low-cost signals about the items being evaluated (e.g., text labels or pictures). We then consider ways of circumventing this problem by comparing agents' reports to ground truth, which is available in practice when there exist trusted evaluators---such as teaching assistants in the peer grading scenario---who can perform a limited number of unbiased (but noisy) evaluations. Of course, when such ground truth is available, a simpler approach is also possible: rewarding each agent based on agreement with ground truth with some probability, and unconditionally rewarding the agent otherwise. Surprisingly, we show that the simpler mechanism achieves stronger incentive guarantees given less access to ground truth than a large set of peer-prediction mechanisms.

cs.GT↗