The utilitarian solution criterion, which has been extensively studied in multi-agent decision making under uncertainty, aims to maximize the sum of individual utilities. However, as the utilitarian solution often discriminates against some agents, it is not desirable for many practical applications where agents have their own interests and fairness is expected. To address this issue, this paper introduces egalitarian solution criteria for sequential decision-making under uncertainty, which are based on the maximin principle. Motivated by different application domains, we propose four maximin fairness criteria and develop corresponding algorithms for computing their optimal policies. Furthermore, we analyze the connections between these criteria and discuss and compare their characteristics.

A scoring rule is a device for eliciting and assessing probabilistic forecasts from an agent. When dealing with continuous outcome spaces, and absent any prior insights into the structure of the agent's beliefs, the rule should allow for a flexible reporting interface that can accurately represent complicated, multi-modal distributions. In this paper, we provide such a scoring rule based on a nonparametric approach of eliciting a set of samples from the agent and efficiently evaluating the score using kernel methods. We prove that sampled reports of increasing size converge rapidly to the true score, and that sampled reports are approximately optimal. We also demonstrate a connection between the scoring rule and the maximum mean discrepancy divergence. Experimental results are provided that confirm rapid convergence and that the expected score correlates well with standard notions of divergence, both important considerations for ensuring that agents are incentivized to report accurate information.

Monte-Carlo Tree Search, especially UCT and its POMDP version POMCP, have demonstrated excellent performanceon many problems. However, to efficiently scale to large domains one should also exploit hierarchical structure if present. In such hierarchical domains, finding rewarded states typically requires to search deeply; covering enough such informative states very far from the root becomes computationally expensive in flat non-hierarchical search approaches. We propose novel, scalable MCTS methods which integrate atask hierarchy into the MCTS framework, specifically lead-ing to hierarchical versions of both, UCT and POMCP. The new method does not need to estimate probabilistic models of each subtask, it instead computes subtask policies purely sample-based. We evaluate the hierarchical MCTS methods on various settings such as a hierarchical MDP, a Bayesian model-based hierarchical RL problem, and a large hierarchical POMDP.

The main computational bottleneck in various sampling based and local-search based inference algorithms for Markov logic networks (e.g., Gibbs sampling, MC-SAT, MaxWalksat, etc.) is computing the number of groundings of a first-order formula that are true given a truth assignment to all of its ground atoms. We reduce this problem to the problem of counting the number of solutions of a constraint satisfaction problem (CSP) and show that during their execution, both sampling based and local-search based algorithms repeatedly solve dynamic versions of this counting problem. Deriving from the vast amount of literature on CSPs and graphical models, we propose an exact junction-tree based algorithm for computing the number of solutions of the dynamic CSP, analyze its properties, and show how it can be used to improve the computational complexity of Gibbs sampling and MaxWalksat. Empirical tests on a variety of benchmarks clearly show that our new approach is several orders of magnitude more scalable than existing approaches.

Lifted probabilistic inference algorithms have been successfully applied to a large number of symmetric graphical models. Unfortunately, the majority of real-world graphical models is asymmetric. This is even the case for relational representations when evidence is given. Therefore, more recent work in the community moved to making the models symmetric and then applying existing lifted inference algorithms. However, this approach has two shortcomings. First, all existing over-symmetric approximations require a relational representation such as Markov logic networks. Second, the induced symmetries often change the distribution significantly, making the computed probabilities highly biased. We present a framework for probabilistic sampling-based inference that only uses the induced approximate symmetries to propose steps in a Metropolis-Hastings style Markov chain. The framework, therefore, leads to improved probability estimates while remaining unbiased. Experiments demonstrate that the approach outperforms existing MCMC algorithms.

We provide a novel, flexible, iterative refinement algorithm to automatically construct an approximate statespace representation for Markov Decision Processes (MDPs). Our approach leverages bisimulation metrics, which have been used in prior work to generate features to represent the state space of MDPs. We address a drawback of this approach, which is the expensive computation of the bisimulation metrics. We propose an algorithm to generate an iteratively improving sequence of state space partitions. Partial metric computations guide the representation search and provide much lower space and computational complexity, while maintaining strong convergence properties. We provide theoretical results guaranteeing convergence as well as experimental illustrations of the accuracy and savings (in time and memory usage) of the new algorithm, compared to traditional bisimulation metric computation.

This paper is about two related decision theoretic problems, nonparametric two-sample testing and independence testing. There is a belief that two recently proposed solutions, based on kernels and distances between pairs of points, behave well in high-dimensional settings. We identify different sources of misconception that give rise to the above belief. Specifically, we differentiate the hardness of estimation of test statistics from the hardness of testing whether these statistics are zero or not, and explicitly discuss a notion of "fair" alternative hypotheses for these problems as dimension increases. We then demonstrate that the power of these tests actually drops polynomially with increasing dimension against fair alternatives. We end with some theoretical insights and shed light on the median heuristic for kernel bandwidth selection. Our work advances the current understanding of the power of modern nonparametric hypothesis tests in high dimensions.

Advice giving has been long explored in artificial intelligence to build robust learning algorithms. We consider advice giving in relational domains where the noise is systematic. The advice is provided as logical statements that are then explicitly considered by the learning algorithm at every update. Our empirical evidence proves that human advice can effectively accelerate learning in noisy structured domains where so far humans have been merely used as labelers or as designers of initial structure of the model.

Bayesian reinforcement learning (BRL) provides a principled framework for optimal exploration-exploitation tradeoff in reinforcement learning. We focus on model based BRL, which involves a compact formulation of the optimal tradeoff from the Bayesian perspective. However, it still remains a computational challenge to compute the Bayes-optimal policy. In this paper, we propose a novel approach to compute tighter value function bounds of the Bayes-optimal value function, which is crucial for improving the performance of many model-based BRL algorithms. We then present how our bounds can be integrated into real-time AO* heuristic search, and provide a theoretical analysis on the impact of improved bounds on the search efficiency. We also provide empirical results on standard BRL domains that demonstrate the effectiveness of our approach.

Two other algorithms require the knowledge Markov Decision Processes (MDPs) offer a general framework of the optimal policy and its expected reward. We show to describe probabilistic planning problems of varying that the expected reward of the optimal policy is a lower complexity. The development of algorithms that act successfully bound for the expected performance of both strategies. in MDPs is important to many AI applications. Our final algorithm switches between the application of Since it is often impossible or intractable to evaluate MDP the optimal policy and the policy with the highest possible algorithms based on a theoretical analysis alone, the International outcome, which can be computed without notable overhead Probabilistic Planning Competition (IPPC) was introduced in the Trial-based Heuristic Tree Search (THTS) framework to allow a comparison based on experimental evaluation. (Keller and Helmert 2013). We show theoretically and empirically The idea is to approximate the quality of an MDP that all algorithms outperform the naïve base approach solver by performing a sequence of runs on a problem instance, that ignores the potential of optimizing evaluation and by using the average of the obtained results as runs in hindsight, and that it pays off to take suboptimal base an approximation of the expected reward.