Abstract In recent years, attention has been focused on the relationship between black-box optimization problem and reinforcement learning problem. In this research, we propose the Mirror Descent Search (MDS) algorithm which is applicable both for black box optimization problems and reinforcement learning problems. Our method is based on the mirror descent method, which is a general optimization algorithm. The contribution of this research is roughly twofold. We propose two essential algorithms, called MDS and Accelerated Mirror Descent Search (AMDS), and two more approximate algorithms: Gaussian Mirror Descent Search (G-MDS) and Gaussian Accelerated Mirror Descent Search (G-AMDS). This research shows that the advanced methods developed in the context of the mirror descent research can be applied to reinforcement learning problem. We also clarify the relationship between an existing reinforcement learning algorithm and our method. With two evaluation experiments, we show our proposed algorithms converge faster than some state-of-the-art methods.
Let us introduce the RKL-based RL algorithms. Relative Entropy Policy Search (REPS) @cite_4 is one of the pioneering algorithms focusing on the information loss during the policy search process. The information loss is defined as the relative entropy, also known as the RKL divergence, between the old policy and the new policy. The new policy is determined under the upper bound constraints of the RKL divergence. Episode-based REPS also considers information loss bound with regard to the upper-level policy @cite_40 . The method is proposed as an extension of REPS to be an episode-based algorithm. The paper @cite_3 discussed the similarity between Episode-based REPS and the proximal point algorithm; they proposed the Online-REPS algorithm as an theoretically guaranteed one. MOdel-based Relative Entropy stochastic search (MORE) also employed RKL divergence @cite_45 , which extends the episode-based REPS to be a model-based RL algorithm. These algorithms employ RKL divergence in their formulation.
@cite_40 @cite_45 @cite_4 @cite_3
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Specifying a numeric reward function for reinforcement learning typically requires a lot of hand-tuning from a human expert. In contrast, preference-based reinforcement learning (PBRL) utilizes only pairwise comparisons between trajectories as a feedback signal, which are often more intuitive to specify. Currently available approaches to PBRL for control problems with continuous state action spaces require a known or estimated model, which is often not available and hard to learn. In this paper, we integrate preference-based estimation of the reward function into a model-free reinforcement learning (RL) algorithm, resulting in a model-free PBRL algorithm. Our new algorithm is based on Relative Entropy Policy Search (REPS), enabling us to utilize stochastic policies and to directly control the greediness of the policy update. REPS decreases exploration of the policy slowly by limiting the relative entropy of the policy update, which ensures that the algorithm is provided with a versatile set of trajectories, and consequently with informative preferences. The preference-based estimation is computed using a sample-based Bayesian method, which can also estimate the uncertainty of the utility. Additionally, we also compare to a linear solvable approximation, based on inverse RL. We show that both approaches perform favourably to the current state-of-the-art. The overall result is an algorithm that can learn non-parametric continuous action policies from a small number of preferences. Policy search is a successful approach to reinforcement learning. However, policy improvements often result in the loss of information. Hence, it has been marred by premature convergence and implausible solutions. As first suggested in the context of covariant policy gradients (Bagnell and Schneider 2003), many of these problems may be addressed by constraining the information loss. In this paper, we continue this path of reasoning and suggest the Relative Entropy Policy Search (REPS) method. The resulting method differs significantly from previous policy gradient approaches and yields an exact update step. It works well on typical reinforcement learning benchmark problems. Path integral (PI) control defines a general class of control problems for which the optimal control computation is equivalent to an inference problem that can be solved by evaluation of a path integral over state trajectories. However, this potential is mostly unused in real-world problems because of two main limitations: first, current approaches can typically only be applied to learn open-loop controllers and second, current sampling procedures are inefficient and not scalable to high dimensional systems. We introduce the efficient Path Integral Relative-Entropy Policy Search (PI-REPS) algorithm for learning feedback policies with PI control. Our algorithm is inspired by information theoretic policy updates that are often used in policy search. We use these updates to approximate the state trajectory distribution that is known to be optimal from the PI control theory. Our approach allows for a principled treatment of different sampling distributions and can be used to estimate many types of parametric or non-parametric feedback controllers. We show that PI-REPS significantly outperforms current methods and is able to solve tasks that are out of reach for current methods. We study the problem of online learning in finite episodic Markov decision processes (MDPs) where the loss function is allowed to change between episodes. The natural performance measure in this learning problem is the regret defined as the difference between the total loss of the best stationary policy and the total loss suffered by the learner. We assume that the learner is given access to a finite action space A and the state space X has a layered structure with L layers, so that state transitions are only possible between consecutive layers. We describe a variant of the recently proposed Relative Entropy Policy Search algorithm and show that its regret after T episodes is 2L|X||A|T log (|X||A| L) in the bandit setting and 2L T log(|X||A| L) in the full information setting, given that the learner has perfect knowledge of the transition probabilities of the underlying MDP. These guarantees largely improve previously known results under much milder assumptions and cannot be significantly improved under general assumptions.