Stochastic Control via Entropy Compression

We consider an agent trying to bring a system to an acceptable state by repeated probabilistic action. Several recent works on algorithmizations of the Lovasz Local Lemma (LLL) can be seen as establishing sufficient conditions for the agent to succeed. Here we study whether such stochastic control is also possible in a noisy environment, where both the process of state-observation and the process of state-evolution are subject to adversarial perturbation (noise). The introduction of noise causes the tools developed for LLL algorithmization to break down since the key LLL ingredient, the sparsity of the causality (dependence) relationship, no longer holds. To overcome this challenge we develop a new analysis where entropy plays a central role, both to measure the rate at which progress towards an acceptable state is made and the rate at which noise undoes this progress. The end result is a sufficient condition that allows a smooth tradeoff between the intensity of the noise and the amenability of the system, recovering an asymmetric LLL condition in the noiseless case.Comment: 18 page

On the Convergence of Techniques that Improve Value Iteration

Prioritisation of Bellman backups or updating only a small subset of actions represent important techniques for speeding up planning in MDPs. The recent literature showed new efficient approaches which exploit these directions. Backward value iteration and backing up only the best actions were shown to lead to a significant reduction of the planning time. This paper conducts a theoretical and empirical analysis of these techniques and shows new important proofs. In particular, (1) it identifies weaker requirements for the convergence of backups based on best actions only, (2) a new method for evaluation of the Bellman error is shown for the update that updates one best action once, (3) it presents the theoretical proof of backward value iteration and establishes required initialisation, (4) and shows that the default state ordering of backups in standard value iteration can significantly influence its performance. Additionally, (5) the existing literature did not compare these methods, either empirically or analytically, against policy iteration. The rigorous empirical and novel theoretical parts of the paper reveal important associations and allow drawing guidelines on which type of value or policy iteration is suitable for a given domain. Finally, our chief message is that standard value iteration can be made far more efficient by simple modifications shown in the paper

Engineering a Conformant Probabilistic Planner

We present a partial-order, conformant, probabilistic planner, Probapop which competed in the blind track of the Probabilistic Planning Competition in IPC-4. We explain how we adapt distance based heuristics for use with probabilistic domains. Probapop also incorporates heuristics based on probability of success. We explain the successes and difficulties encountered during the design and implementation of Probapop

Contingent planning under uncertainty via stochastic satisfiability

We describe a new planning technique that efficiently solves probabilistic propositional contingent planning problems by converting them into instances of stochastic satisfiability (SSAT) and solving these problems instead. We make fundamental contributions in two areas: the solution of SSAT problems and the solution of stochastic planning problems. This is the first work extending the planning-as-satisfiability paradigm to stochastic domains. Our planner, ZANDER, can solve arbitrary, goal-oriented, finite-horizon partially observable Markov decision processes (POMDPs). An empirical study comparing ZANDER to seven other leading planners shows that its performance is competitive on a range of problems. © 2003 Elsevier Science B.V. All rights reserved

Combined optimization algorithms applied to pattern classification

Accurate classification by minimizing the error on test samples is the main goal in pattern classification. Combinatorial optimization is a well-known method for solving minimization problems, however, only a few examples of classifiers axe described in the literature where combinatorial optimization is used in pattern classification. Recently, there has been a growing interest in combining classifiers and improving the consensus of results for a greater accuracy. In the light of the "No Ree Lunch Theorems", we analyse the combination of simulated annealing, a powerful combinatorial optimization method that produces high quality results, with the classical perceptron algorithm. This combination is called LSA machine. Our analysis aims at finding paradigms for problem-dependent parameter settings that ensure high classifica, tion results. Our computational experiments on a large number of benchmark problems lead to results that either outperform or axe at least competitive to results published in the literature. Apart from paxameter settings, our analysis focuses on a difficult problem in computation theory, namely the network complexity problem. The depth vs size problem of neural networks is one of the hardest problems in theoretical computing, with very little progress over the past decades. In order to investigate this problem, we introduce a new recursive learning method for training hidden layers in constant depth circuits. Our findings make contributions to a) the field of Machine Learning, as the proposed method is applicable in training feedforward neural networks, and to b) the field of circuit complexity by proposing an upper bound for the number of hidden units sufficient to achieve a high classification rate. One of the major findings of our research is that the size of the network can be bounded by the input size of the problem and an approximate upper bound of 8 + √2n/n threshold gates as being sufficient for a small error rate, where n := log/SL and SL is the training set