Recent successes of value-based multi-agent deep reinforcement learning employ optimism by limiting underestimation updates of value function estimator, through carefully controlled learning rate (, 2017) or reduced update probability (, 2018). To achieve full cooperation when learning independently, an agent must estimate the state values contingent on having optimal teammates; therefore, value overestimation is frequency injected to counteract negative effects caused by unobservable teammate sub-optimal policies and explorations. Aiming to solve this issue through automatic scheduling, this paper introduces a decentralized quantile estimator, which we found empirically to be more stable, sample efficient and more likely to converge to the joint optimal policy.
Hysteretic Deep Q-Network (HDQN) @cite_4 applies HQL to DQN. Using DQN as basis, TD error is given by @math . For simplicity, HDQN first sets a base learning rate @math suitable for the network (e.g. @math ), and scales the learning rate into @math and @math . In practice, HDQN usually fixes @math at @math and tunes @math and @math instead. Thus, in the following discussions, we only discuss the choice and effect of @math (the decrease rate) under the assumption that @math .
@cite_4
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Deep Reinforcement Learning methods have achieved state of the art performance in learning control policies for the games in the Atari 2600 domain. One of the important parameters in the Arcade Learning Environment (ALE) is the frame skip rate. It decides the granularity at which agents can control game play. A frame skip value of @math allows the agent to repeat a selected action @math number of times. The current state of the art architectures like Deep Q-Network (DQN) and Dueling Network Architectures (DuDQN) consist of a framework with a static frame skip rate, where the action output from the network is repeated for a fixed number of frames regardless of the current state. In this paper, we propose a new architecture, Dynamic Frame skip Deep Q-Network (DFDQN) which makes the frame skip rate a dynamic learnable parameter. This allows us to choose the number of times an action is to be repeated based on the current state. We show empirically that such a setting improves the performance on relatively harder games like Seaquest. Instability and variability of Deep Reinforcement Learning (DRL) algorithms tend to adversely affect their performance. Averaged-DQN is a simple extension to the DQN algorithm, based on averaging previously learned Q-values estimates, which leads to a more stable training procedure and improved performance by reducing approximation error variance in the target values. To understand the effect of the algorithm, we examine the source of value function estimation errors and provide an analytical comparison within a simplified model. We further present experiments on the Arcade Learning Environment benchmark that demonstrate significantly improved stability and performance due to the proposed extension. Existing cellular network analyses, and even simulations, typically use the standard path loss model where received power decays like @math over a distance @math . This standard path loss model is quite idealized, and in most scenarios the path loss exponent @math is itself a function of @math , typically an increasing one. Enforcing a single path loss exponent can lead to orders of magnitude differences in average received and interference powers versus the true values. In this paper, we study multi-slope path loss models, where different distance ranges are subject to different path loss exponents. We focus on the dual-slope path loss function, which is a piece-wise power law and continuous and accurately approximates many practical scenarios. We derive the distributions of SIR, SNR, and finally SINR before finding the potential throughput scaling, which provides insight on the observed cell-splitting rate gain. The exact mathematical results show that the SIR monotonically decreases with network density, while the converse is true for SNR, and thus the network coverage probability in terms of SINR is maximized at some finite density. With ultra-densification (network density goes to infinity), there exists a phase transition in the near-field path loss exponent @math : if @math unbounded potential throughput can be achieved asymptotically; if $ 0 , ultra-densification leads in the extreme case to zero throughput. It is common practice to decay the learning rate. Here we show one can usually obtain the same learning curve on both training and test sets by instead increasing the batch size during training. This procedure is successful for stochastic gradient descent (SGD), SGD with momentum, Nesterov momentum, and Adam. It reaches equivalent test accuracies after the same number of training epochs, but with fewer parameter updates, leading to greater parallelism and shorter training times. We can further reduce the number of parameter updates by increasing the learning rate @math and scaling the batch size @math . Finally, one can increase the momentum coefficient @math and scale @math , although this tends to slightly reduce the test accuracy. Crucially, our techniques allow us to repurpose existing training schedules for large batch training with no hyper-parameter tuning. We train Inception-ResNet-V2 on ImageNet to @math validation accuracy in under 2500 parameter updates, efficiently utilizing training batches of 65536 images.