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We consider the problem of efficient inference of the Average Treatment Effect in a sequential experiment where the policy governing the assignment of subjects to treatment or control can change over time. We first provide a central limit…
We introduce a "high probability" framework for repeated games with incomplete information. In our non-equilibrium setting, players aim to guarantee a certain payoff with high probability, rather than in expected value. We provide a high…
Consider the following heuristic for building a decision tree for a function $f : \{0,1\}^n \to \{\pm 1\}$. Place the most influential variable $x_i$ of $f$ at the root, and recurse on the subfunctions $f_{x_i=0}$ and $f_{x_i=1}$ on the…
The Wald development of statistical decision theory addresses decision making with sample data. Wald's concept of a statistical decision function (SDF) embraces all mappings of the form [data -> decision]. An SDF need not perform…
Recent advancements in algorithms for sequential decision-making under imperfect information have shown remarkable success in large games such as limit- and no-limit poker. These algorithms traditionally formalize the games using the…
A candidate explanation of the good empirical performance of deep neural networks is the implicit regularization effect of first order optimization methods. Inspired by this, we prove a convergence theorem for nonconvex composite…
Let $T\_n$ denote the set of unrooted labeled trees of size $n$ and let $T\_n$ be a particular (finite, unlabeled) tree. Assuming that every tree of $T\_n$ is equally likely, it is shown that the limiting distribution as $n$ goes to…
In the context of tree-search stochastic planning algorithms where a generative model is available, we consider on-line planning algorithms building trees in order to recommend an action. We investigate the question of avoiding re-planning…
Decision trees and random forest remain highly competitive for classification on medium-sized, standard datasets due to their robustness, minimal preprocessing requirements, and interpretability. However, a single tree suffers from high…
In a satisficing equilibrium each agent $i$ plays one of her top $k_i$ actions in response to the actions of the other agents. Our concept unifies models of bounded rationality and yields predictions that differ from canonical solution…
Although recent work in AI has made great progress in solving large, zero-sum, extensive-form games, the underlying assumption in most past work is that the parameters of the game itself are known to the agents. This paper deals with the…
Certain families of combinatorial objects admit recursive descriptions in terms of generating trees: each node of the tree corresponds to an object, and the branch leading to the node encodes the choices made in the construction of the…
Behavior trees represent a modular way to create an overall controller from a set of sub-controllers solving different sub-problems. These sub-controllers can be created in different ways, such as classical model based control or…
Standard rational expectations models with an occasionally binding zero lower bound constraint either admit no solutions (incoherence) or multiple solutions (incompleteness). This paper shows that deviations from full-information rational…
We state and prove Kuhn's equivalence theorem for a new representation of games, the intrinsic form. First, we introduce games in intrinsic form where information is represented by $\sigma$-fields over a product set. For this purpose, we…
We study the problem of learning a good set of policies, so that when combined together, they can solve a wide variety of unseen reinforcement learning tasks with no or very little new data. Specifically, we consider the framework of…
It is well known that reinforcement learning can be cast as inference in an appropriate probabilistic model. However, this commonly involves introducing a distribution over agent trajectories with probabilities proportional to exponentiated…
Algorithms for model checking and satisfiability of the modal $\mu$-calculus start by converting formulas to alternating parity tree automata. Thus, model checking is reduced to checking acceptance by tree automata and satisfiability to…
Automata for unordered unranked trees are relevant for defining schemas and queries for data trees in Json or Xml format. While the existing notions are well-investigated concerning expressiveness, they all lack a proper notion of…
Crawford's et al. (2021) article on estimation of discrete choice models with unobserved or latent consideration sets, presents a unified framework to address the problem in practice by using "sufficient sets", defined as a combination of…