314,355 research outputs found
On the Convergence and Sample Complexity Analysis of Deep Q-Networks with -Greedy Exploration
This paper provides a theoretical understanding of Deep Q-Network (DQN) with
the -greedy exploration in deep reinforcement learning. Despite
the tremendous empirical achievement of the DQN, its theoretical
characterization remains underexplored. First, the exploration strategy is
either impractical or ignored in the existing analysis. Second, in contrast to
conventional Q-learning algorithms, the DQN employs the target network and
experience replay to acquire an unbiased estimation of the mean-square Bellman
error (MSBE) utilized in training the Q-network. However, the existing
theoretical analysis of DQNs lacks convergence analysis or bypasses the
technical challenges by deploying a significantly overparameterized neural
network, which is not computationally efficient. This paper provides the first
theoretical convergence and sample complexity analysis of the practical setting
of DQNs with -greedy policy. We prove an iterative procedure with
decaying converges to the optimal Q-value function geometrically.
Moreover, a higher level of values enlarges the region of
convergence but slows down the convergence, while the opposite holds for a
lower level of values. Experiments justify our established
theoretical insights on DQNs
Comparative Study of Reinforcement Learning Algorithms: Deep Q-Networks, Deep Deterministic Policy Gradients and Proximal Policy Optimization
The advancement of Artificial Intelligence (AI), particularly in the field of Reinforcement Learning (RL), has led to significant breakthroughs in numerous domains, ranging from autonomous systems to complex game environments. Among this progress, the emergence and evolution of algorithms like Deep Q-Networks (DQN), Deep Deterministic Policy Gradients (DDPG), and Proximal Policy Optimization (PPO) have been pivotal. These algorithms, each with unique approaches and strengths, have become fundamental in tackling diverse RL challenges. This study aims to dissect and compare these three influential algorithms to provide a clearer understanding of their mechanics, efficiencies, and applicability. We delve into the theoretical underpinnings of DQN, DDPG, and PPO, and assess their performances across a variety of standard benchmarks. Through this comparative analysis, we seek to offer valuable insights for choosing the right algorithms for different environments and highlight potential pathways for future research in the field of Reinforcement Learning
Machine learning detects terminal singularities
Algebraic varieties are the geometric shapes defined by systems of polynomial
equations; they are ubiquitous across mathematics and science. Amongst these
algebraic varieties are Q-Fano varieties: positively curved shapes which have
Q-factorial terminal singularities. Q-Fano varieties are of fundamental
importance in geometry as they are "atomic pieces" of more complex shapes - the
process of breaking a shape into simpler pieces in this sense is called the
Minimal Model Programme. Despite their importance, the classification of Q-Fano
varieties remains unknown. In this paper we demonstrate that machine learning
can be used to understand this classification. We focus on 8-dimensional
positively-curved algebraic varieties that have toric symmetry and Picard rank
2, and develop a neural network classifier that predicts with 95% accuracy
whether or not such an algebraic variety is Q-Fano. We use this to give a first
sketch of the landscape of Q-Fanos in dimension 8. How the neural network is
able to detect Q-Fano varieties with such accuracy remains mysterious, and
hints at some deep mathematical theory waiting to be uncovered. Furthermore,
when visualised using the quantum period, an invariant that has played an
important role in recent theoretical developments, we observe that the
classification as revealed by ML appears to fall within a bounded region, and
is stratified by the Fano index. This suggests that it may be possible to state
and prove conjectures on completeness in the future. Inspired by the ML
analysis, we formulate and prove a new global combinatorial criterion for a
positively curved toric variety of Picard rank 2 to have terminal
singularities. Together with the first sketch of the landscape of Q-Fanos in
higher dimensions, this gives new evidence that machine learning can be an
essential tool in developing mathematical conjectures and accelerating
theoretical discovery.Comment: 20 pages, 11 figures, 3 table
Provable and Practical: Efficient Exploration in Reinforcement Learning via Langevin Monte Carlo
We present a scalable and effective exploration strategy based on Thompson
sampling for reinforcement learning (RL). One of the key shortcomings of
existing Thompson sampling algorithms is the need to perform a Gaussian
approximation of the posterior distribution, which is not a good surrogate in
most practical settings. We instead directly sample the Q function from its
posterior distribution, by using Langevin Monte Carlo, an efficient type of
Markov Chain Monte Carlo (MCMC) method. Our method only needs to perform noisy
gradient descent updates to learn the exact posterior distribution of the Q
function, which makes our approach easy to deploy in deep RL. We provide a
rigorous theoretical analysis for the proposed method and demonstrate that, in
the linear Markov decision process (linear MDP) setting, it has a regret bound
of , where is the dimension of the
feature mapping, is the planning horizon, and is the total number of
steps. We apply this approach to deep RL, by using Adam optimizer to perform
gradient updates. Our approach achieves better or similar results compared with
state-of-the-art deep RL algorithms on several challenging exploration tasks
from the Atari57 suite
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