640831
Finite-Sample Convergence Rates for Q-Learning and Indirect Algorithms
In this paper, we address two issues of long-standing interest in the reinforcement learning literature. First, what kinds of performance guarantees can be made for Q-learning after only a finite number of actions? Second, what quantitative comparisons can be made between Q-learning and model-based (indirect) approaches, which use experience to estimate next-state distributions for off-line value iteration? 
 
We first show that both Q-learning and the indirect approach enjoy rather rapid convergence to the optimal policy as a function of the number of state transitions observed. In particular, on the order of only (N log(1/e)/e2)(log(N) + loglog(l/e)) transitions are sufficient for both algorithms to come within e of the optimal policy, in an idealized model that assumes the observed transitions are "well-mixed" throughout an N-state MDP. Thus, the two approaches have roughly the same sample complexity. Perhaps surprisingly, this sample complexity is far less than what is required for the model-based approach to actually construct a good approximation to the next-state distribution. The result also shows that the amount of memory required by the model-based approach is closer to N than to N2. 
 
For either approach, to remove the assumption that the observed transitions are well-mixed, we consider a model in which the transitions are determined by a fixed, arbitrary exploration policy. Bounds on the number of transitions required in order to achieve a desired level of performance are then related to the stationary distribution and mixing time of this policy.
6543846
Predictive state representations with options
Recent work on predictive state representation (PSR) models has focused on using predictions of the outcomes of open-loop action sequences as state. These predictions answer questions of the form "What is the probability of seeing observation sequence o1, o2, ..., oN if the agent takes action sequence a1, a2, ..., aN from some given history?" We would like to ask more expressive questions in our representation of state, such as "If I behave according to some policy until I terminate, what will be my last observation?" We extend the linear PSR framework to answer questions like these about options -- temporally extended, closed-loop courses of action -- bounding the size of the linear PSR needed to model questions about a certain class of options. We introduce a hierarchical PSR (HPSR) that can make predictions about both options and primitive action sequences and show empirical results from learning HPSRs in simple domains.
17854729
Reinforcement Learning Algorithms for Average-Payoff Markovian Decision Processes
Reinforcement learning (RL) has become a central paradigm for solving learning-control problems in robotics and artificial intelligence. RL researchers have focussed almost exclusively on problems where the controller has to maximize the discounted sum of payoffs. However, as emphasized by Schwartz (1993), in many problems, e.g., those for which the optimal behavior is a limit cycle, it is more natural and computationally advantageous to formulate tasks so that the controller's objective is to maximize the average payoff received per time step. In this paper I derive new average-payoff RL algorithms as stochastic approximation methods for solving the system of equations associated with the policy evaluation and optimal control questions in average-payoff RL tasks. These algorithms are analogous to the popular TD and Q-learning algorithms already developed for the discounted-payoff case. One of the algorithms derived here is a significant variation of Schwartz's R-learning algorithm. Preliminary empirical results are presented to validate these new algorithms.
211724543
An Upper Bound on the Loss from Approximate Optimal-Value Functions
2661414
Graphical Models for Game Theory
We introduce a compact graph-theoretic representation for multi-party game theory. Our main result is a provably correct and efficient algorithm for computing approximate Nash equilibria in one-stage games represented by trees or sparse graphs.
9771856
Nash Convergence of Gradient Dynamics in General-Sum Games
Multi-agent games are becoming an increasingly prevalent formalism for the study of electronic commerce and auctions. The speed at which transactions can take place and the growing complexity of electronic marketplaces makes the study of computationally simple agents an appealing direction. In this work, we analyze the behavior of agents that incrementally adapt their strategy through gradient ascent on expected payoff, in the simple setting of two-player, two-action, iterated general-sum games, and present a surprising result. We show that either the agents will converge to a Nash equilibrium, or if the strategies themselves do not converge, then their average payoffs will nevertheless converge to the payoffs of a Nash equilibrium.
206599449
Downloading vs Purchase: Music Industry vs Consumers
The music industry argues that unauthorised downloading of music is detrimentally affecting the industry; a breach of copyright that needs to be stopped. The industry has taken many actions to stamp out unauthorised music downloading, including prosecution of peer-to-peer software users for breach of copyright and against peer-to-peer software suppliers for contributory copyright infringement. Industry commentators have questioned this line of reasoning particularly as there is now significant revenue from legal music downloads in the United States and Europe. This paper draws on a qualitative study of music consumers in Australia to show there is not a clear dichotomy between down- loading and purchase. It is more of a continuum. From the users' perspective, downloading is transformed to the activity of accessing and exploring music. The industry could more fruitfully focus on satisfying this basic aspect of the listening experience in DRM systems in order to work together with their customers.
14183054
Framed-quadtree path planning for mobile robots operating in sparse environments
Mobile robots operating in vast outdoor unstructured environments often only have incomplete maps and must deal with new objects found during traversal. Path planning in such sparsely occupied regions must be incremental to accommodate new information, and, must use efficient representations. In previous work we have developed an optimal method D* to plan paths when the environment is not known ahead of time, but, rather is discovered as the robot moves around. To date, D* has been applied to a uniform grid representation for obstacles and free space. In this paper we propose the use of D* with framed quadtrees to improve the efficiency of planning paths in sparse environments. The new system has been tested in simulation as well on an autonomous jeep, equipped with local obstacle avoidance capabilities. We show how the use of framed quadtrees improves performance in terms of path length, computation speed, and memory requirements.
853906
Analytical Mean Squared Error Curves for Temporal Difference Learning
We provide analytical expressions governing changes to the bias and variance of the lookup table estimators provided by various Monte Carlo and temporal difference value estimation algorithms with offline updates over trials in absorbing Markov reward processes. We have used these expressions to develop software that serves as an analysis tool: given a complete description of a Markov reward process, it rapidly yields an exact mean-square-error curve, the curve one would get from averaging together sample mean-square-error curves from an infinite number of learning trials on the given problem. We use our analysis tool to illustrate classes of mean-square-error curve behavior in a variety of example reward processes, and we show that although the various temporal difference algorithms are quite sensitive to the choice of step-size and eligibility-trace parameters, there are values of these parameters that make them similarly competent, and generally good.
45020911
Using unconstrained elite archives for multiobjective optimization
Multiobjective evolutionary algorithms (MOEAs) have been the subject of numerous studies over the past 20 years. Recent work has highlighted the use of an active archive of elite, nondominated solutions to improve the optimization speed of these algorithms. However, preserving all elite individuals is costly in time (due to the linear comparison with all archived solutions needed before a new solution can be inserted into the archive). Maintaining an elite population of a fixed maximum size (by clustering or other means) alleviates this problem, but can cause retreating (or oscillitory) and shrinking estimated Pareto fronts - which can affect the efficiency of the search process. New data structures are introduced to facilitate the use of an unconstrained elite archive, without the need for a linear comparison to the elite set for every new individual inserted. The general applicability of these data structures is shown by their use in an evolution-strategy-based MOEA and a genetic-algorithm-based MOEA. It is demonstrated that MOEAs using the new data structures run significantly faster than standard, unconstrained archive MOEAs, and result in estimated Pareto fronts significantly ahead of MOEAs using a constrained archive. It is also shown that the use of an unconstrained elite archive permits robust criteria for algorithm termination to be used, and that the use of the data structure can also be used to increase the speed of algorithms using /spl epsi/-dominance methods.
2924964
Exploiting heterogeneity in sensor networks
The presence of heterogeneous nodes (i.e., nodes with an enhanced energy capacity or communication capability) in a sensor network is known to increase network reliability and lifetime. However, questions of where how many, and what types of heterogeneous resources to deploy remain largely unexplored. We focus on energy and link heterogeneity in ad hoc sensor networks and consider resource-aware MAC and routing protocols to utilize those resources. Using analysis, simulation, and real testbed measurements, we evaluate the impact of number and placement of heterogeneous resources on performance in networks of different sizes and densities. While we prove that optimal deployment is very hard in general, we also show that only a modest number of reliable, long-range backhaul links and line-powered nodes are required to have a significant impact. Properly deployed, heterogeneity can triple the average delivery rate and provide a 5-fold increase in the lifetime (respectively) of a large batten-powered network of simple sensors.