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.
Works related to non-stationary MDPs such as @cite_4 @cite_15 , which deal only with changes in reward function, are more associated with RL alone than with a hybrid method such as oASP(MDP), since RL methods are already capable of handling changes in the reward and transition functions. The advantage of ASP is to find the set of states so that it is possible to search for an optimal solution regardless of the agent's transition and reward functions.
@cite_15 @cite_4
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This article addresses a particular Transfer Reinforcement Learning (RL) problem: when dynamics do not change from one task to another, and only the reward function does. Our method relies on two ideas, the first one is that transition samples obtained from a task can be reused to learn on any other task: an immediate reward estimator is learnt in a supervised fashion and for each sample, the reward entry is changed by its reward estimate. The second idea consists in adopting the optimism in the face of uncertainty principle and to use upper bound reward estimates. Our method is tested on a navigation task, under four Transfer RL experimental settings: with a known reward function, with strong and weak expert knowledge on the reward function, and with a completely unknown reward function. It is also evaluated in a Multi-Task RL experiment and compared with the state-of-the-art algorithms. Results reveal that this method constitutes a major improvement for transfer multi-task problems that share dynamics. We consider a Markov decision process (MDP) setting in which the reward function is allowed to change after each time step (possibly in an adversarial manner), yet the dynamics remain fixed. Similar to the experts setting, we address the question of how well an agent can do when compared to the reward achieved under the best stationary policy over time. We provide efficient algorithms, which have regret bounds with no dependence on the size of state space. Instead, these bounds depend only on a certain horizon time of the process and logarithmically on the number of actions. The main contribution of this paper consists in extending several non-stationary Reinforcement Learning (RL) algorithms and their theoretical guarantees to the case of discounted zero-sum Markov Games (MGs).As in the case of Markov Decision Processes (MDPs), non-stationary algorithms are shown to exhibit better performance bounds compared to their stationary counterparts. The obtained bounds are generically composed of three terms: 1) a dependency over gamma (discount factor), 2) a concentrability coefficient and 3) a propagation error term. This error, depending on the algorithm, can be caused by a regression step, a policy evaluation step or a best-response evaluation step. As a second contribution, we empirically demonstrate, on generic MGs (called Garnets), that non-stationary algorithms outperform their stationary counterparts. In addition, it is shown that their performance mostly depends on the nature of the propagation error. Indeed, algorithms where the error is due to the evaluation of a best-response are penalized (even if they exhibit better concentrability coefficients and dependencies on gamma) compared to those suffering from a regression error. 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.