Automatic Probabilistic Program Verification through Random Variable Abstraction

The weakest pre-expectation calculus has been proved to be a mature theory to analyze quantitative properties of probabilistic and nondeterministic programs. We present an automatic method for proving quantitative linear properties on any denumerable state space using iterative backwards fixed point calculation in the general framework of abstract interpretation. In order to accomplish this task we present the technique of random variable abstraction (RVA) and we also postulate a sufficient condition to achieve exact fixed point computation in the abstract domain. The feasibility of our approach is shown with two examples, one obtaining the expected running time of a probabilistic program, and the other the expected gain of a gambling strategy. Our method works on general guarded probabilistic and nondeterministic transition systems instead of plain pGCL programs, allowing us to easily model a wide range of systems including distributed ones and unstructured programs. We present the operational and weakest precondition semantics for this programs and prove its equivalence

Modelling Emotion Based Reward Valuation with Computational Reinforcement Learning

We show that computational reinforcement learning can model human decision making in the Iowa Gambling Task (IGT). The IGT is a card game, which tests decision making under uncertainty. In our experiments, we found that modulating learning rate decay in Q-learning, enables the approximation of both the behaviour of normal subjects and those who are emotionally impaired by ventromedial prefrontal lesions. Outcomes observed in impaired subjects are modeled by high learning rate decay, while low learning rate decay replicates healthy subjects under otherwise identical conditions. The ventromedial prefrontal cortex has been associated with emotion based reward valuation, and, the value function in reinforcement learning provides an analogous assessment mechanism. Thus reinforcement learning can provide a good model for the role of emotional reward as a modulator of the learning rate

Simulated annealing algorithm for optimal capital growth

We investigate the problem of dynamic optimal capital growth of a portfolio. A general framework that one strives to maximize the expected logarithm utility of long term growth rate was developed. Exact optimization algorithms run into difficulties in this framework and this motivates the investigation of applying simulated annealing optimized algorithm to optimize the capital growth of a given portfolio. Empirical results with real financial data indicate that the approach is inspiring for capital growth portfolio

Quantum Games and Programmable Quantum Systems

Attention to the very physical aspects of information characterizes the current research in quantum computation, quantum cryptography and quantum communication. In most of the cases quantum description of the system provides advantages over the classical approach. Game theory, the study of decision making in conflict situation has already been extended to the quantum domain. We would like to review the latest development in quantum game theory that is relevant to information processing. We will begin by illustrating the general idea of a quantum game and methods of gaining an advantage over "classical opponent". Then we review the most important game theoretical aspects of quantum information processing. On grounds of the discussed material, we reason about possible future development of quantum game theory and its impact on information processing and the emerging information society. The idea of quantum artificial intelligence is explained.

Cakewalk Sampling

We study the task of finding good local optima in combinatorial optimization problems. Although combinatorial optimization is NP-hard in general, locally optimal solutions are frequently used in practice. Local search methods however typically converge to a limited set of optima that depend on their initialization. Sampling methods on the other hand can access any valid solution, and thus can be used either directly or alongside methods of the former type as a way for finding good local optima. Since the effectiveness of this strategy depends on the sampling distribution, we derive a robust learning algorithm that adapts sampling distributions towards good local optima of arbitrary objective functions. As a first use case, we empirically study the efficiency in which sampling methods can recover locally maximal cliques in undirected graphs. Not only do we show how our adaptive sampler outperforms related methods, we also show how it can even approach the performance of established clique algorithms. As a second use case, we consider how greedy algorithms can be combined with our adaptive sampler, and we demonstrate how this leads to superior performance in k-medoid clustering. Together, these findings suggest that our adaptive sampler can provide an effective strategy to combinatorial optimization problems that arise in practice.Comment: Accepted as a conference paper by AAAI-2020 (oral presentation