Restricted Value Iteration: Theory and Algorithms

Value iteration is a popular algorithm for finding near optimal policies for POMDPs. It is inefficient due to the need to account for the entire belief space, which necessitates the solution of large numbers of linear programs. In this paper, we study value iteration restricted to belief subsets. We show that, together with properly chosen belief subsets, restricted value iteration yields near-optimal policies and we give a condition for determining whether a given belief subset would bring about savings in space and time. We also apply restricted value iteration to two interesting classes of POMDPs, namely informative POMDPs and near-discernible POMDPs

Sequential Selection of Correlated Ads by POMDPs

Online advertising has become a key source of revenue for both web search engines and online publishers. For them, the ability of allocating right ads to right webpages is critical because any mismatched ads would not only harm web users' satisfactions but also lower the ad income. In this paper, we study how online publishers could optimally select ads to maximize their ad incomes over time. The conventional offline, content-based matching between webpages and ads is a fine start but cannot solve the problem completely because good matching does not necessarily lead to good payoff. Moreover, with the limited display impressions, we need to balance the need of selecting ads to learn true ad payoffs (exploration) with that of allocating ads to generate high immediate payoffs based on the current belief (exploitation). In this paper, we address the problem by employing Partially observable Markov decision processes (POMDPs) and discuss how to utilize the correlation of ads to improve the efficiency of the exploration and increase ad incomes in a long run. Our mathematical derivation shows that the belief states of correlated ads can be naturally updated using a formula similar to collaborative filtering. To test our model, a real world ad dataset from a major search engine is collected and categorized. Experimenting over the data, we provide an analyse of the effect of the underlying parameters, and demonstrate that our algorithms significantly outperform other strong baselines

Markov Decision Processes with Applications in Wireless Sensor Networks: A Survey

Wireless sensor networks (WSNs) consist of autonomous and resource-limited devices. The devices cooperate to monitor one or more physical phenomena within an area of interest. WSNs operate as stochastic systems because of randomness in the monitored environments. For long service time and low maintenance cost, WSNs require adaptive and robust methods to address data exchange, topology formulation, resource and power optimization, sensing coverage and object detection, and security challenges. In these problems, sensor nodes are to make optimized decisions from a set of accessible strategies to achieve design goals. This survey reviews numerous applications of the Markov decision process (MDP) framework, a powerful decision-making tool to develop adaptive algorithms and protocols for WSNs. Furthermore, various solution methods are discussed and compared to serve as a guide for using MDPs in WSNs

Operational Decision Making under Uncertainty: Inferential, Sequential, and Adversarial Approaches

Modern security threats are characterized by a stochastic, dynamic, partially observable, and ambiguous operational environment. This dissertation addresses such complex security threats using operations research techniques for decision making under uncertainty in operations planning, analysis, and assessment. First, this research develops a new method for robust queue inference with partially observable, stochastic arrival and departure times, motivated by cybersecurity and terrorism applications. In the dynamic setting, this work develops a new variant of Markov decision processes and an algorithm for robust information collection in dynamic, partially observable and ambiguous environments, with an application to a cybersecurity detection problem. In the adversarial setting, this work presents a new application of counterfactual regret minimization and robust optimization to a multi-domain cyber and air defense problem in a partially observable environment