Coherent frequentism

By representing the range of fair betting odds according to a pair of confidence set estimators, dual probability measures on parameter space called frequentist posteriors secure the coherence of subjective inference without any prior distribution. The closure of the set of expected losses corresponding to the dual frequentist posteriors constrains decisions without arbitrarily forcing optimization under all circumstances. This decision theory reduces to those that maximize expected utility when the pair of frequentist posteriors is induced by an exact or approximate confidence set estimator or when an automatic reduction rule is applied to the pair. In such cases, the resulting frequentist posterior is coherent in the sense that, as a probability distribution of the parameter of interest, it satisfies the axioms of the decision-theoretic and logic-theoretic systems typically cited in support of the Bayesian posterior. Unlike the p-value, the confidence level of an interval hypothesis derived from such a measure is suitable as an estimator of the indicator of hypothesis truth since it converges in sample-space probability to 1 if the hypothesis is true or to 0 otherwise under general conditions.Comment: The confidence-measure theory of inference and decision is explicitly extended to vector parameters of interest. The derivation of upper and lower confidence levels from valid and nonconservative set estimators is formalize

The Assistive Multi-Armed Bandit

Learning preferences implicit in the choices humans make is a well studied problem in both economics and computer science. However, most work makes the assumption that humans are acting (noisily) optimally with respect to their preferences. Such approaches can fail when people are themselves learning about what they want. In this work, we introduce the assistive multi-armed bandit, where a robot assists a human playing a bandit task to maximize cumulative reward. In this problem, the human does not know the reward function but can learn it through the rewards received from arm pulls; the robot only observes which arms the human pulls but not the reward associated with each pull. We offer sufficient and necessary conditions for successfully assisting the human in this framework. Surprisingly, better human performance in isolation does not necessarily lead to better performance when assisted by the robot: a human policy can do better by effectively communicating its observed rewards to the robot. We conduct proof-of-concept experiments that support these results. We see this work as contributing towards a theory behind algorithms for human-robot interaction.Comment: Accepted to HRI 201

Reinforcement Learning via AIXI Approximation

This paper introduces a principled approach for the design of a scalable general reinforcement learning agent. This approach is based on a direct approximation of AIXI, a Bayesian optimality notion for general reinforcement learning agents. Previously, it has been unclear whether the theory of AIXI could motivate the design of practical algorithms. We answer this hitherto open question in the affirmative, by providing the first computationally feasible approximation to the AIXI agent. To develop our approximation, we introduce a Monte Carlo Tree Search algorithm along with an agent-specific extension of the Context Tree Weighting algorithm. Empirically, we present a set of encouraging results on a number of stochastic, unknown, and partially observable domains.Comment: 8 LaTeX pages, 1 figur

Model and Reinforcement Learning for Markov Games with Risk Preferences

We motivate and propose a new model for non-cooperative Markov game which considers the interactions of risk-aware players. This model characterizes the time-consistent dynamic "risk" from both stochastic state transitions (inherent to the game) and randomized mixed strategies (due to all other players). An appropriate risk-aware equilibrium concept is proposed and the existence of such equilibria is demonstrated in stationary strategies by an application of Kakutani's fixed point theorem. We further propose a simulation-based Q-learning type algorithm for risk-aware equilibrium computation. This algorithm works with a special form of minimax risk measures which can naturally be written as saddle-point stochastic optimization problems, and covers many widely investigated risk measures. Finally, the almost sure convergence of this simulation-based algorithm to an equilibrium is demonstrated under some mild conditions. Our numerical experiments on a two player queuing game validate the properties of our model and algorithm, and demonstrate their worth and applicability in real life competitive decision-making.Comment: 38 pages, 6 tables, 5 figure

An empirical learning-based validation procedure for simulation workflow

Simulation workflow is a top-level model for the design and control of simulation process. It connects multiple simulation components with time and interaction restrictions to form a complete simulation system. Before the construction and evaluation of the component models, the validation of upper-layer simulation workflow is of the most importance in a simulation system. However, the methods especially for validating simulation workflow is very limit. Many of the existing validation techniques are domain-dependent with cumbersome questionnaire design and expert scoring. Therefore, this paper present an empirical learning-based validation procedure to implement a semi-automated evaluation for simulation workflow. First, representative features of general simulation workflow and their relations with validation indices are proposed. The calculation process of workflow credibility based on Analytic Hierarchy Process (AHP) is then introduced. In order to make full use of the historical data and implement more efficient validation, four learning algorithms, including back propagation neural network (BPNN), extreme learning machine (ELM), evolving new-neuron (eNFN) and fast incremental gaussian mixture model (FIGMN), are introduced for constructing the empirical relation between the workflow credibility and its features. A case study on a landing-process simulation workflow is established to test the feasibility of the proposed procedure. The experimental results also provide some useful overview of the state-of-the-art learning algorithms on the credibility evaluation of simulation models