Uncertain Actions Research Articles

Solving quantified constraint satisfaction problems

We make a number of contributions to the study of the Quantified Constraint Satisfaction Problem (QCSP). The QCSP is an extension of the constraint satisfaction problem that can be used to model combinatorial problems containing contingency or uncertainty. It allows for universally quantified variables that can model uncertain actions and events, such as the unknown weather for a future party, or an opponent's next move in a game. In this paper we report significant contributions to two very different methods for solving QCSPs. The first approach is to implement special purpose algorithms for QCSPs; and the second is to encode QCSPs as Quantified Boolean Formulas and then use specialized QBF solvers. The discovery of particularly effective encodings influenced the design of more effective algorithms: by analyzing the properties of these encodings, we identify the features in QBF solvers responsible for their efficiency. This enables us to devise analogues of these features in QCSPs, and implement them in special purpose algorithms, yielding an effective special purpose solver, QCSP-Solve. Experiments show that this solver and a highly optimized QBF encoding are several orders of magnitude more efficient than the initially developed algorithms. A final, but significant, contribution is the identification of flaws in simple methods of generating random QCSP instances, and a means of generating instances which are not known to be flawed.

Sequential Monte Carlo in reachability heuristics for probabilistic planning

Some of the current best conformant probabilistic planners focus on finding a fixed length plan with maximal probability. While these approaches can find optimal solutions, they often do not scale for large problems or plan lengths. As has been shown in classical planning, heuristic search outperforms bounded length search (especially when an appropriate plan length is not given a priori). The problem with applying heuristic search in probabilistic planning is that effective heuristics are as yet lacking. In this work, we apply heuristic search to conformant probabilistic planning by adapting planning graph heuristics developed for non-deterministic planning. We evaluate a straight-forward application of these planning graph techniques, which amounts to exactly computing a distribution over many relaxed planning graphs (one planning graph for each joint outcome of uncertain actions at each time step). Computing this distribution is costly, so we apply Sequential Monte Carlo (SMC) to approximate it. One important issue that we explore in this work is how to automatically determine the number of samples required for effective heuristic computation. We empirically demonstrate on several domains how our efficient, but sometimes suboptimal, approach enables our planner to solve much larger problems than an existing optimal bounded length probabilistic planner and still find reasonable quality solutions.

Public-Private Partnership (PPP) as a Social Game

Discrepancy between social demands and public resources has become apparent in many countries worldwide. Institutions and industries involved in public services seek new forms of collaboration and combine all available public and private skills to circumvent problems. Advocates of public-private partnership (PPP) assess the progress as convincing. Reserved observers argue that the technique has immanent weaknesses. Putting the phenomena, experience, and discussion into a wider context of gaming helps to arrive at a better comprehension. The paper focuses on road transportation infrastructure issues but its conclusions are of broader interest. Four perspectives are chosen to discuss PPP as a gaming issue. Linguistics, the mathematical theory of games, experimental psychology and the theory of institutions offer useful analytical concepts, theorems and approaches. The gaming perspective allows us to identify and define more clearly several uncertain or misinterpreted situations or actions experienced in PPP implementations. The conceptual identification of positions, motivations and further characteristics is not only possible but helps all partners to better understand the structure, the rules and roles given in the procedure. Use of the gaming perspective in PPP issues seems to enhance 'fair play'. Expected trends of development and further areas of suggested research are derived from the conclusions and conjectures. Application of the gaming perspective is recommended in the development of project delivery techniques, education and training.

Survey of decision field theory

This article summarizes the cumulative progress of a cognitive-dynamical approach to decision making and preferential choice called decision field theory. This review includes applications to (a) binary decisions among risky and uncertain actions, (b) multi-attribute preferential choice, (c) multi-alternative preferential choice, and (d) certainty equivalents such as prices. The theory provides natural explanations for violations of choice principles including strong stochastic transitivity, independence of irrelevant alternatives, and regularity. The theory also accounts for the relation between choice and decision time, preference reversals between choice and certainty equivalents, and preference reversals under time pressure. Comparisons with other dynamic models of decision-making and other random utility models of preference are discussed.

Optimal Selection of Uncertain Actions by Maximizing Expected Utility

A new means of action selection via utility fusion is introduced as an alternative to both sensor fusion and command fusion. Distributed asynchronous behaviors indicate the utility of various possible states and their associated uncertainty. A centralized arbiter then combines these utilities and probabilities to determine the optimal action based on the maximization of expected utility. The construction of a utility map allows the system being controlled to be modeled and compensated fors experimental results verify that this approach improves performance.

Tactical problems involving uncertain actions

The purpose of this paper is to solve anm-silent versusn-silent duel with arbitrary accuracy functionsP andQ which are continuously differentiable in [0, 1] with positive derivatives in (0, 1) and such thatP(0)=Q(0)=0,P(1)∈(0, 1),Q(1)∈(0, 1). The game can be interpreted as a game in which the players know only that the numbers of their actions have binomial distribution.

The mixed temporal game 1×1 with uncertain actions

Author's introduction: game solved in the present paper belongs to a class of temporal games whose general model was given by S. Karlin [Mathematical methods and theory in games, programming and economics, Addison-Wesley, Reading, Mass., 1959; MR0111634]. The rules are as follows. There are two opposing players, A and B. Each player has a certain number of actions which he can take in the time interval [0,1]. Neither player knows the number of actions he or his opposer has. Each player knows only the distribution of the number of actions for him and his opponent. More precisely, let k1 denote the number of actions of player A and k2 the number of actions of player B, and let k1 and k2 be independent random variables. The distributions of these random variables are as follows: P(k1=1)=p, P(k1=0)=1−p, P(k2=1)=q, P(k2=0)=1−q, p,q∈(0,1]. The opponent knows only both distributions. Thus player A [player B] knows beforehand that he as well as his opponent has zero or one action with the probability given above. If player A has an action then it is silent, i.e., his opponent does not know the moment when the action is taken. If player B has an action it is noisy, i.e. his opponent knows the moment when the action is taken. As a result of the action the player can win or, equivalently, his opponent can lose. A win can be achieved according to the probability given above. If player A [player B] takes an action at time t, then the probability of winning is equal to P(t) [to Q(t)]. Functions P(t) and Q(t) are called payoff functions. These functions satisfy the following conditions: (1) P(t) and Q(t) are differentiable and P′(t)>0 and Q′(t)>0 for t∈(0,1); (2) P(0)=Q(0)=0, P(1)=Q(1)=1. Both functions are known to the players before the game begins. The game ends when one player wins or when neither wins at time t=1. If only player A wins he obtains the payoff +1 from his opponent, and likewise if only B wins he obtains the payoff +1. In the remaining cases the payoff is equal to zero. Y. Teraoka solved a temporal game 1×1 with uncertain actions [Rep. Himeji Inst. Tech. 28 (1975), 1–8; RŽMat 1976:8 V662]. If in the game, played according to the rules given above, we put p=q=1, then this type of game is a particular case of the game solved by A. Styszynski [Zastos. Mat. 14 (1974), 205–225; MR0351487]. Here we present a solution to a more generalized game in which the first player has n actions. The game defined above can be interpreted as a duel. In the course of an action shots are fired and a win is achieved when the opponent is hit. The payoff function is then called an accuracy function. The duelists do not know beforehand whether the weapons are loaded or accurate. They know only the probability of drawing a loaded weapon. We shall use this interpretation in later sections of the paper. This game can also be viewed as an advertising Two enterprises are engaged in an advertising war to win a contract. Here an action can be viewed as setting in motion the advertising machine of the player's company. A win is achieved when the contract is awarded to the player's company as a result of his action. Before the campaign the players do not know whether they will receive funds from their central offices to engage in the advertising war.