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Motivated by the episodic version of the classical inventory control problem, we propose a new Q-learning-based algorithm, Elimination-Based Half-Q-Learning (HQL), that enjoys improved efficiency over existing algorithms for a wide variety of problems in the one-sided-feedback setting. We also provide a simpler variant of the algorithm, Full-Q-Learning (FQL), for the full-feedback setting. We establish that HQL incurs $ tilde{mathcal{O}}(H^3sqrt{ T})$ regret and FQL incurs $tilde{mathcal{O}}(H^2sqrt{ T})$ regret, where $H$ is the length of each episode and $T$ is the total length of the horizon. The regret bounds are not affected by the possibly huge state and action space. Our numerical experiments demonstrate the superior efficiency of HQL and FQL, and the potential to combine reinforcement learning with richer feedback models.
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In this paper, we establish a theoretical comparison between the asymptotic mean-squared error of Double Q-learning and Q-learning. Our result builds upon an analysis for linear stochastic approximation based on Lyapunov equations and applies to both tabular setting and with linear function approximation, provided that the optimal policy is unique and the algorithms converge. We show that the asymptotic mean-squared error of Double Q-learning is exactly equal to that of Q-learning if Double Q-learning uses twice the learning rate of Q-learning and outputs the average of its two estimators. We also present some practical implications of this theoretical observation using simulations.
This work extends the analysis of the theoretical results presented within the paper Is Q-Learning Provably Efficient? by Jin et al. We include a survey of related research to contextualize the need for strengthening the theoretical guarantees related to perhaps the most important threads of model-free reinforcement learning. We also expound upon the reasoning used in the proofs to highlight the critical steps leading to the main result showing that Q-learning with UCB exploration achieves a sample efficiency that matches the optimal regret that can be achieved by any model-based approach.
Task offloading is an emerging technology in fog-enabled networks. It allows users to transmit tasks to neighbor fog nodes so as to utilize the computing resources of the networks. In this paper, we investigate a stochastic task offloading model and propose a multi-armed bandit framework to formulate this model. We consider the fact that different helper nodes prefer different kinds of tasks. Further, we assume each helper node just feeds back one-bit information to the task node to indicate the level of happiness. The key challenge of this problem lies in the exploration-exploitation tradeoff. We thus implement a UCB-type algorithm to maximize the long-term happiness metric. Numerical simulations are given in the end of the paper to corroborate our strategy.
In this paper, we first study the problem of combinatorial pure exploration with full-bandit feedback (CPE-BL), where a learner is given a combinatorial action space $mathcal{X} subseteq {0,1}^d$, and in each round the learner pulls an action $x in mathcal{X}$ and receives a random reward with expectation $x^{top} theta$, with $theta in mathbb{R}^d$ a latent and unknown environment vector. The objective is to identify the optimal action with the highest expected reward, using as few samples as possible. For CPE-BL, we design the first {em polynomial-time adaptive} algorithm, whose sample complexity matches the lower bound (within a logarithmic factor) for a family of instances and has a light dependence of $Delta_{min}$ (the smallest gap between the optimal action and sub-optimal actions). Furthermore, we propose a novel generalization of CPE-BL with flexible feedback structures, called combinatorial pure exploration with partial linear feedback (CPE-PL), which encompasses several families of sub-problems including full-bandit feedback, semi-bandit feedback, partial feedback and nonlinear reward functions. In CPE-PL, each pull of action $x$ reports a random feedback vector with expectation of $M_{x} theta $, where $M_x in mathbb{R}^{m_x times d}$ is a transformation matrix for $x$, and gains a random (possibly nonlinear) reward related to $x$. For CPE-PL, we develop the first {em polynomial-time} algorithm, which simultaneously addresses limited feedback, general reward function and combinatorial action space, and provide its sample complexity analysis. Our empirical evaluation demonstrates that our algorithms run orders of magnitude faster than the existing ones, and our CPE-BL algorithm is robust across different $Delta_{min}$ settings while our CPE-PL algorithm is the only one returning correct answers for nonlinear reward functions.
There were many algorithms to substitute the back-propagation (BP) in the deep neural network (DNN) training. However, they could not become popular because their training accuracy and the computational efficiency were worse than BP. One of them was direct feedback alignment (DFA), but it showed low training performance especially for the convolutional neural network (CNN). In this paper, we overcome the limitation of the DFA algorithm by combining with the conventional BP during the CNN training. To improve the training stability, we also suggest the feedback weight initialization method by analyzing the patterns of the fixed random matrices in the DFA. Finally, we propose the new training algorithm, binary direct feedback alignment (BDFA) to minimize the computational cost while maintaining the training accuracy compared with the DFA. In our experiments, we use the CIFAR-10 and CIFAR-100 dataset to simulate the CNN learning from the scratch and apply the BDFA to the online learning based object tracking application to examine the training in the small dataset environment. Our proposed algorithms show better performance than conventional BP in both two different training tasks especially when the dataset is small.
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