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Register a new userOnline Learning for Unknown Partially Observable MDPs
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Added by
Mehdi Jafarnia-Jahromi
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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Solving Partially Observable Markov Decision Processes (POMDPs) is hard. Learning optimal controllers for POMDPs when the model is unknown is harder. Online learning of optimal controllers for unknown POMDPs, which requires efficient learning using regret-minimizing algorithms that effectively tradeoff exploration and exploitation, is even harder, and no solution exists currently. In this paper, we consider infinite-horizon average-cost POMDPs with unknown transition model, though a known observation model. We propose a natural posterior sampling-based reinforcement learning algorithm (PSRL-POMDP) and show that it achieves a regret bound of $O(log T)$, where $T$ is the time horizon, when the parameter set is finite. In the general case (continuous parameter set), we show that the algorithm achieves $O (T^{2/3})$ regret under two technical assumptions. To the best of our knowledge, this is the first online RL algorithm for POMDPs and has sub-linear regret.
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We consider the problem of learning in episodic finite-horizon Markov decision processes with an unknown transition function, bandit feedback, and adversarial losses. We propose an efficient algorithm that achieves $mathcal{tilde{O}}(L|X|sqrt{|A|T})$ regret with high probability, where $L$ is the horizon, $|X|$ is the number of states, $|A|$ is the number of actions, and $T$ is the number of episodes. To the best of our knowledge, our algorithm is the first to ensure $mathcal{tilde{O}}(sqrt{T})$ regret in this challenging setting; in fact it achieves the same regret bound as (Rosenberg & Mansour, 2019a) that considers an easier setting with full-information feedback. Our key technical contributions are two-fold: a tighter confidence set for the transition function, and an optimistic loss estimator that is inversely weighted by an $textit{upper occupancy bound}$.
This paper deals with bandit online learning problems involving feedback of unknown delay that can emerge in multi-armed bandit (MAB) and bandit convex optimization (BCO) settings. MAB and BCO require only values of the objective function involved that become available through feedback, and are used to estimate the gradient appearing in the corresponding iterative algorithms. Since the challenging case of feedback with emph{unknown} delays prevents one from constructing the sought gradient estimates, existing MAB and BCO algorithms become intractable. For such challenging setups, delayed exploration, exploitation, and exponential (DEXP3) iterations, along with delayed bandit gradient descent (DBGD) iterations are developed for MAB and BCO, respectively. Leveraging a unified analysis framework, it is established that the regret of DEXP3 and DBGD are ${cal O}big( sqrt{Kbar{d}(T+D)} big)$ and ${cal O}big( sqrt{K(T+D)} big)$, respectively, where $bar{d}$ is the maximum delay and $D$ denotes the delay accumulated over $T$ slots. Numerical tests using both synthetic and real data validate the performance of DEXP3 and DBGD.
Bounded agents are limited by intrinsic constraints on their ability to process information that is available in their sensors and memory and choose actions and memory updates. In this dissertation, we model these constraints as information-rate constraints on communication channels connecting these various internal components of the agent. We make four major contributions detailed below and many smaller contributions detailed in each section. First, we formulate the problem of optimizing the agent under both extrinsic and intrinsic constraints and develop the main tools for solving it. Second, we identify another reason for the challenging convergence properties of the optimization algorithm, which is the bifurcation structure of the update operator near phase transitions. Third, we study the special case of linear-Gaussian dynamics and quadratic cost (LQG), where the optimal solution has a particularly simple and solvable form. Fourth, we explore the learning task, where the model of the world dynamics is unknown and sample-based updates are used instead.
Reinforcement Learning (RL) agents typically learn memoryless policies---policies that only consider the last observation when selecting actions. Learning memoryless policies is efficient and optimal in fully observable environments. However, some form of memory is necessary when RL agents are faced with partial observability. In this paper, we study a lightweight approach to tackle partial observability in RL. We provide the agent with an external memory and additional actions to control what, if anything, is written to the memory. At every step, the current memory state is part of the agents observation, and the agent selects a tuple of actions: one action that modifies the environment and another that modifies the memory. When the external memory is sufficiently expressive, optimal memoryless policies yield globally optimal solutions. Unfortunately, previous attempts to use external memory in the form of binary memory have produced poor results in practice. Here, we investigate alternative forms of memory in support of learning effective memoryless policies. Our novel forms of memory outperform binary and LSTM-based memory in well-established partially observable domains.
We study linear contextual bandits with access to a large, confounded, offline dataset that was sampled from some fixed policy. We show that this problem is closely related to a variant of the bandit problem with side information. We construct a linear bandit algorithm that takes advantage of the projected information, and prove regret bounds. Our results demonstrate the ability to take advantage of confounded offline data. Particularly, we prove regret bounds that improve current bounds by a factor related to the visible dimensionality of the contexts in the data. Our results indicate that confounded offline data can significantly improve online learning algorithms. Finally, we demonstrate various characteristics of our approach through synthetic simulations.
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