Non-stationary domains, that change in unpredicted ways, are a challenge for agents searching for optimal policies in sequential decision-making problems. This paper presents a combination of Markov Decision Processes (MDP) with Answer Set Programming (ASP), named Online ASP for MDP (oASP(MDP)), which is a method capable of constructing the set of domain states while the agent interacts with a changing environment. oASP(MDP) updates previously obtained policies, learnt by means of Reinforcement Learning (RL), using rules that represent the domain changes observed by the agent. These rules represent a set of domain constraints that are processed as ASP programs reducing the search space. Results show that oASP(MDP) is capable of finding solutions for problems in non-stationary domains without interfering with the action-value function approximation process.
Previous attempts at combining RL with ASP include @cite_3 , which proposes the use of ASP to find a pre-defined plan for a RL agent. This plan is described as a hierarchical MDP and RL is used to find the optimal policy for this MDP. However, changes in the environment, as used in the present work, were not considered in @cite_3 .
@cite_3
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Reinforcement learning (RL) agents have traditionally been tasked with maximizing the value function of a Markov decision process (MDP), either in continuous settings, with fixed discount factor @math , or in episodic settings, with @math . While this has proven effective for specific tasks with well-defined objectives (e.g., games), it has never been established that fixed discounting is suitable for general purpose use (e.g., as a model of human preferences). This paper characterizes rationality in sequential decision making using a set of seven axioms and arrives at a form of discounting that generalizes traditional fixed discounting. In particular, our framework admits a state-action dependent "discount" factor that is not constrained to be less than 1, so long as there is eventual long run discounting. Although this broadens the range of possible preference structures in continuous settings, we show that there exists a unique "optimizing MDP" with fixed @math whose optimal value function matches the true utility of the optimal policy, and we quantify the difference between value and utility for suboptimal policies. Our work can be seen as providing a normative justification for (a slight generalization of) Martha White's RL task formalism (2017) and other recent departures from the traditional RL, and is relevant to task specification in RL, inverse RL and preference-based RL. Robots deployed to assist and collaborate with humans in complex domains need the ability to represent and reason with incomplete domain knowledge, and to learn from minimal feedback obtained from non-expert human participants. This paper presents an architecture that combines the complementary strengths of Reinforcement Learning (RL) and declarative programming to support such commonsense reasoning and incremental learning of the rules governing the domain dynamics. Answer Set Prolog (ASP), a declarative language, is used to represent domain knowledge. The robot’s current beliefs, obtained by inference in the ASP program, are used to formulate the task of learning previously unknown domain rules as an RL problem. The learned rules are, in turn, encoded in the ASP program and used to plan action sequences for subsequent tasks. The architecture is illustrated and evaluated in the context of a simulated robot that plans action sequences to arrange tabletop objects in desired configurations. We use single-agent and multi-agent Reinforcement Learning (RL) for learning dialogue policies in a resource allocation negotiation scenario. Two agents learn concurrently by interacting with each other without any need for simulated users (SUs) to train against or corpora to learn from. In particular, we compare the Qlearning, Policy Hill-Climbing (PHC) and Win or Learn Fast Policy Hill-Climbing (PHC-WoLF) algorithms, varying the scenario complexity (state space size), the number of training episodes, the learning rate, and the exploration rate. Our results show that generally Q-learning fails to converge whereas PHC and PHC-WoLF always converge and perform similarly. We also show that very high gradually decreasing exploration rates are required for convergence. We conclude that multiagent RL of dialogue policies is a promising alternative to using single-agent RL and SUs or learning directly from corpora. In this semi-tutorial paper, we first review the information-theoretic approach to account for the computational costs incurred during the search for optimal actions in a sequential decision-making problem. The traditional (MDP) framework ignores computational limitations while searching for optimal policies, essentially assuming that the acting agent is perfectly rational and aims for exact optimality. Using the free-energy, a variational principle is introduced that accounts not only for the value of a policy alone, but also considers the cost of finding this optimal policy. The solution of the variational equations arising from this formulation can be obtained using familiar Bellman-like value iterations from dynamic programming (DP) and the Blahut-Arimoto (BA) algorithm from rate distortion theory. Finally, we demonstrate the utility of the approach for generating hierarchies of state abstractions that can be used to best exploit the available computational resources. A numerical example showcases these concepts for a path-planning problem in a grid world environment.