University of Liverpool


Model-Based Reinforcement Learning under Periodical Observability

AAAI Conferences

The uncertainty induced by unknown attacker locations is one of the problems in deploying AI methods to security domains. We study a model with partial observability of the attacker location and propose a novel reinforcement learning method using partial information about attacker behaviour coming from the system. This method is based on deriving beliefs about underlying states using Bayesian inference. These beliefs are then used in the QMDP algorithm. We particularly design the algorithm for spatial security games, where the defender faces intelligent and adversarial opponents.


Constructing a Standard Model: Lessons from CHREST

AAAI Conferences

Although it might be too early for a standard model of the mind (SMM), comparison between current cognitive architectures is a useful exercise. This article highlights some of the likely difficulties facing the development of a SMM – both empirical and theoretical. In particular, it follows Newell (1990) by arguing that a viable model of the mind must be constructed taking advantage of experimental constraints, based on comparisons of the model with (human or animal) data. We then describe our proposed methodology for ensuring a tight link between psychological data and a cognitive architecture. We also discuss CHREST, a cognitive model with a particular emphasis on modelling psychological results. CHREST has been applied in several domains, such as language acquisition and expertise. The article concludes by highlighting some of the features that distinguish CHREST from architectures such as Soar and ACT-R. Some of these differences are significant, creating challenges for a SMM.



Query Answering in DL-Lite with Datatypes: A Non-Uniform Approach

AAAI Conferences

Adding datatypes to ontology-mediated queries (OMQs) often makes query answering hard. As a consequence, the use of datatypes in OWL 2 QL has been severely restricted. In this paper we propose a new, non-uniform, way of analyzing the data-complexity of OMQ answering with datatypes. Instead of restricting the ontology language we aim at a classification of the patterns of datatype atoms in OMQs into those that can occur in non-tractable OMQs and those that only occur in tractable OMQs. To this end we establish a close link between OMQ answering with datatypes and constraint satisfaction problems over the datatypes. In a case study we apply this link to prove a P/coNP-dichotomy for OMQs over DL-Lite extended with the datatype (Q,<=). The proof employs a recent dichotomy result by Bodirsky and Kára for temporal constraint satisfaction problems.


Constrained Pure Nash Equilibria in Polymatrix Games

AAAI Conferences

We study the problem of checking for the existence of constrained pure Nash equilibria in a subclass of polymatrix games defined on weighted directed graphs. The payoff of a player is defined as the sum of nonnegative rational weights on incoming edges from players who picked the same strategy augmented by a fixed integer bonus for picking a given strategy. These games capture the idea of coordination within a local neighbourhood in the absence of globally common strategies. We study the decision problem of checking whether a given set of strategy choices for a subset of the players is consistent with some pure Nash equilibrium or, alternatively, with all pure Nash equilibria. We identify the most natural tractable cases and show NP or coNP-completness of these problems already for unweighted DAGs.


The Computational Complexity of Weighted Greedy Matching

AAAI Conferences

Motivated by the fact that in several cases a matching in a graph is stable if and only if it is produced by a greedy algorithm, we study the problem of computing a maximum weight greedy matching on weighted graphs, termed GREEDYMATCHING. In wide contrast to the maximum weight matching problem, for which many efficient algorithms are known, we prove that GREEDYMATCHING is strongly NP-hard and APX-complete, and thus it does not admit a PTAS unless P=NP, even on graphs with maximum degree at most 3 and with at most three different integer edge weights. Furthermore we prove that GREEDYMATCHING is strongly NP-hard if the input graph is in addition bipartite. Moreover we consider three natural parameters of the problem, for which we establish a sharp threshold behavior between NP-hardness and computational tractability. On the positive side, we present a randomized approximation algorithm (RGMA) for GREEDYMATCHING on a special class of weighted graphs, called bushgraphs. We highlight an unexpected connection between RGMA and the approximation of maximum cardinality matching in unweighted graphs via randomized greedy algorithms. We show that, if the approximation ratio of RGMA is ρ, then for every ε > 0 the randomized MRG algorithm of (Aronson et al. 1995) gives a (ρ − ε)-approximation for the maximum cardinality matching. We conjecture that a tightbound for ρ is 2/3; we prove our conjecture true for four subclasses of bush graphs. Proving a tight bound for the approximation ratio of MRG on unweighted graphs (and thus also proving a tight value for ρ) is a long-standing open problem (Poloczek and Szegedy 2012). This unexpected relation of our RGMA algorithm with the MRG algorithm may provide new insights for solving this problem.


Maximizing the Probability of Arriving on Time: A Practical Q-Learning Method

AAAI Conferences

The stochastic shortest path problem is of crucial importance for the development of sustainable transportation systems. Existing methods based on the probability tail model seek for the path that maximizes the probability of arriving at the destination before a deadline. However, they suffer from low accuracy and/or high computational cost. We design a novel Q-learning method where the converged Q-values have the practical meaning as the actual probabilities of arriving on time so as to improve accuracy. By further adopting dynamic neural networks to learn the value function, our method can scale well to large road networks with arbitrary deadlines. Experimental results on real road networks demonstrate the significant advantages of our method over other counterparts.


A Model for Learning Description Logic Ontologies Based on Exact Learning

AAAI Conferences

We investigate the problem of learning description logic (DL) ontologies in Angluin et al.’s framework of exact learning via queries posed to an oracle. We consider membership queries of the form “is a tuple a of individuals a certain answer to a data retrieval query q in a given ABox and the unknown target ontology?” and completeness queries of the form “does a hypothesis ontology entail the unknown target ontology?” Given a DL L and a data retrieval query language Q, we study polynomial learnability of ontologies in L using data retrieval queries in Q and provide an almost complete classification for DLs that are fragments of EL with role inclusions and of DL-Lite and for data retrieval queries that range from atomic queries and EL/ELI-instance queries to conjunctive queries. Some results are proved by non-trivial reductions to learning from subsumption examples.


Limiting Logical Violations in Ontology Alignnment Through Negotiation

AAAI Conferences

Ontology alignment (also called ontology matching) is the process of identifying correspondences between entities in different, possibly heterogeneous, ontologies. Traditional ontology alignment techniques rely on the full disclosure of the ontological models; however, within open and opportunistic environments, such approaches may not always be pragmatic or even acceptable (due to privacy concerns). Several studies have focussed on collaborative, decentralised approaches to ontology alignment, where agents negotiate the acceptability of single correspondences acquired from past encounters, or try to ascertain novel correspondences on the fly. However, such approaches can lead to logical violations that may undermine their utility. In this paper, we extend a dialogical approach to correspondence negotiation, whereby agents not only exchange details of possible correspondences, but also identify potential violations to the consistency and conservativity principles. We present a formal model of the dialogue, and show how agents can repair logical violations during the dialogue by invoking a correspondence repair, thus negotiating and exchanging repair plans. We illustrate this opportunistic alignment mechanism with an example and we empirically show that allowing agents to strategically reject or weaken correspondences when these cause violations does not degrade the effectiveness of the alignment computed, whilst reducing the number of residual violations.


A Semantical Analysis of Second-Order Propositional Modal Logic

AAAI Conferences

This paper is aimed as a contribution to the use of formal modal languages in Artificial Intelligence. We introduce a multi-modal version of Second-order Propositional Modal Logic (SOPML), an extension of modal logic with propositional quantification, and illustrate its usefulness as a specification language for knowledge representation as well as temporal and spatial reasoning. Then, we define novel notions of (bi)simulation and prove that these preserve the interpretation of SOPML formulas. Finally, we apply these results to assess the expressive power of SOPML.