Algorithm learns Nash equilibria in stochastic games using entropy-regularized policies.
problem Learning Nash equilibria in zero-sum stochastic games is computationally expensive.
method Entropy-regularized soft policies for Q-function updates.
result Algorithm converges to Nash equilibrium under certain conditions.
The paper analyzes Q-learning in 2-player Markov games and provides gap-dependent logarithmic regret bounds.
problem Analyzing the cumulative regret of Nash Q-learning in 2-player turn-based stochastic Markov games.
method Proposed gap-dependent logarithmic upper bounds for cumulative regret in episodic tabular setting and discounted game setting.
result The proposed bounds match theoretical lower bounds up to a logarithmic term.
Model-free learning for multi-agent stochastic games is an active area of research. Existing reinforcement learning algorithms, however, are often restricted to zero-sum games, and are applicable only in small state-action spaces or other simplified settings. Here, we develop a new data efficient Deep-Q-learning method…
Agents trained with reinforcement learning deviate from Nash equilibrium in optimal execution game.
problem Deviation of reinforcement learning strategies from Nash equilibrium in optimal execution game.
method Two-player optimal execution game with reinforcement learning algorithms (Double Deep Q-Learning).
result Strategies learned by agents deviate significantly from Nash equilibrium, exhibiting supra-competitive solutions.
Study shows market makers can cooperate without communication.
problem Concerns of collusion in AI-driven market-making.
method Formulated as a repeated game, studied with Q-learning.
result Market makers can learn cooperative strategies without communication.
Paper optimizes reinforcement learning in self-play games with reduced steps.
problem Optimizing reinforcement learning algorithms for self-play in two-player zero-sum games.
method Proposes optimistic Nash Q-learning and Nash V-learning algorithms with improved sample complexity.
result Achieves sample complexity of O(SAB) for Nash Q-learning and O(S(A+B)) for Nash V-learning, closing the gap with lower bounds. A new algorithm reduces memory and computational needs for reinforcement learning.
problem Memory and computational inefficiency in model-free reinforcement learning.
method Memory-Efficient Nash Q-Learning (ME-Nash-QL) for two-player zero-sum games.
result Proves ME-Nash-QL reduces space and sample complexity for tabular and long-horizon cases.
Consider a two-player zero-sum stochastic game where the transition function can be embedded in a given feature space. We propose a two-player Q-learning algorithm for approximating the Nash equilibrium strategy via sampling. The algorithm is shown to find an ε-optimal strategy using sample size linear to the number …
V-learning tackles multiagent reinforcement learning by reducing sample complexity.
problem Curse of multiagents in multiagent reinforcement learning.
method V-learning is a fully decentralized algorithm that learns Nash, correlated, and coarse correlated equilibria.
result V-learning achieves sample complexity that scales with the maximum number of actions per agent, not the joint action space.
Paper presents a GMFG framework for large stochastic games.
problem Learning Nash Equilibrium in large stochastic games.
method Value-based and policy-based reinforcement learning algorithms with smoothed policies.
result Proposed algorithms GMF-V and GMF-P are efficient and robust in GMFG setting.
The paper analyzes RL in high-frequency market making with theoretical and practical implications.
problem Applying RL to high-frequency market making with theoretical rigor.
method Theoretical analysis bridging RL and financial economics, focusing on sampling frequency effects.
result An interesting tradeoff between error and complexity in RL algorithms as sampling frequency decreases.
New bounds for SA with arbitrary norm contractions and Markovian noise.
problem Finite-time analysis of two-time-scale stochastic approximation with arbitrary norm contractions and Markovian noise.
method Use of generalized Moreau envelope for arbitrary norm contractions and solutions of Poisson equation for Markovian noise.
result Mean square error decays at rates of O(1/n2/3) and O(1/n) under different conditions. Double Q-learning has the same mean-squared error as Q-learning under certain conditions.
problem Comparing the mean-squared error of Double Q-learning and Q-learning.
method Theoretical analysis based on Lyapunov equations for both tabular and linear function approximation settings.
result The asymptotic mean-squared error of Double Q-learning is exactly equal to that of Q-learning under specific conditions.
DE-QT detects optimal Q-learning stopping points.
problem Information loss in Q-learning during prolonged training.
method Introducing DE-QT to detect entropy changes in Q-tables.
result DE-QT identifies the best stopping point for Q-learning.
Let M and N be Nash manifolds, and f and g Nash maps from M to N. If M and N are compact and if f and g are analytically R-L equivalent, then they are Nash R-L equivalent. In the local case, Cinfty R-L equivalence of two Nash map germs implies Nash R-L equivalence. This shows a difference of Nash…
This paper analyzes momentum Q-learning with finite-sample guarantees.
problem Improving Q-learning performance with momentum schemes.
method Proposes MomentumQ algorithm integrating Nesterov and Polyak's momentum schemes, analyzes convergence for function approximations.
result Establishes finite-sample convergence rates for MomentumQ, demonstrating better performance than vanilla Q-learning.
EBQL reduces bias in Q-learning for improved performance.
problem Over- and under-estimation biases in Q-learning degrade performance.
method Ensemble Bootstrapping to reduce both over- and under-estimation biases.
result EBQL outperforms other Q-learning methods in Atari games.
PQ-learning improves Q-learning by periodically updating target estimates.
problem Improving sample complexity in Q-learning for finding optimal policies.
method Maintains two Q-value estimates, one online and one target, updated periodically.
result PQ-learning achieves better sample complexity for finding epsilon-optimal policies.
New self-imitation learning method improves performance in continuous control tasks.
problem Improving off-policy learning in continuous control tasks.
method Proposes a n-step lower bound to generalize lower-bound Q-learning and introduces a new family of self-imitation learning algorithms.
result n-step lower bound Q-learning achieves a better trade-off between bias and contraction rate, leading to improved performance.
Linear Q-learning converges to a bounded set without divergence.
problem Proving linear Q-learning does not diverge and converges to a bounded set.
method No modifications to the original linear Q-learning algorithm, no Bellman completeness or near-optimality assumptions, only an ε-softmax behavior policy with adaptive temperature.
result First L2 convergence rate of linear Q-learning iterates to a bounded set. Q-learning with neural network function approximation (neural Q-learning for short) is among the most prevalent deep reinforcement learning algorithms. Despite its empirical success, the non-asymptotic convergence rate of neural Q-learning remains virtually unknown. In this paper, we present a finite-time analysis of a…
Nash's theorem proved with Günther's trick
problem Proving Nash's smooth embedding theorem
method Using Günther's trick
result Nash's theorem proved
Q-learning requires more samples than minimax bounds suggest for optimal Q-function approximation.
problem Understanding the sample complexity of Q-learning in synchronous settings.
method Analyzing Q-learning in synchronous MDPs with state and action spaces, proving minimax optimal sample complexity for TD learning and Q-learning under certain conditions.
result Q-learning requires more samples than minimax bounds suggest, revealing strict sub-optimality when action space is more than one.
Q-learning for average cost MDPs gets a concentration bound.
problem Finding bounds for Q-learning in average cost MDPs.
method Derives a concentration bound using shortest path problem equivalence.
result Numerical comparison with relative value iteration shows the bound's effectiveness.
New algorithm uses Whittle index to improve Q-learning for restless bandits.
problem Optimizing decision-making in multiarmed restless bandits with average reward.
method Introduces a novel reinforcement learning algorithm combining Q-learning and Whittle index policy.
result Demonstrates significant computational gains and excellent empirical performance.
We propose local symplectic surgery, a two-timescale procedure for finding local Nash equilibria in two-player zero-sum games. We first show that previous gradient-based algorithms cannot guarantee convergence to local Nash equilibria due to the existence of non-Nash stationary points. By taking advantage of the differ…
Machine learning detects NASH patients from medical claims data.
problem Detecting undiagnosed NASH patients for screening and management.
method Gradient-boosted decision trees trained on administrative medical claims data.
result Model precision for NASH detection is significantly higher than NASH incidence.
LBQL improves Q-learning by using lookahead bounds for better performance.
problem Improving Q-learning in stochastic environments.
method LBQL uses lookahead bounds to construct dual penalties and track upper and lower bounds via stochastic approximation.
result LBQL converges faster and is more robust to hyperparameters than standard Q-learning.
This paper analyzes how periodic and soft target updates stabilize linear Q-learning.
problem Theoretical explanation of stabilization mechanisms for linear Q-learning.
method Exact analysis using switched linear system dynamics and the joint spectral radius.
result Periodic and soft target updates can guarantee convergence to the exact projected Q-Bellman solution under specific conditions.
Optimal geometric estimates for Kähler manifolds with bounded Nash entropy
problem Optimal geometric estimates for compact Kähler manifolds
method Proving Sobolev-type inequality and local volume noncollapsing with optimal exponents
result Uniformly bounded q-Nash entropy Kernelized Q-learning achieves good performance with minimal data.
problem Efficient Q-learning in high-dimensional spaces.
method Kernelized Q-learning framework with effective dimensionality.
result Concrete regret bounds for linear and Gaussian RBF kernels.
Paper addresses underestimation bias in double Q-learning, proposing a method to improve learning performance.
problem Underestimation bias in double Q-learning leading to non-optimal fixed points.
method Proposes a simple approach using approximate dynamic programming to bound the target value.
result Significant improvement in learning performance over baseline algorithms in Atari benchmark tasks.
The paper examines Nash equilibrium in GANs for stationary Gaussian processes.
problem Existence and uniqueness of Nash equilibrium in GANs for stationary Gaussian processes.
method Analyzes the existence of Nash equilibrium in GANs for stationary Gaussian processes, considering different discriminator families.
result The existence of Nash equilibrium depends on the discriminator family and symmetry properties of the generator family.
New algorithm reduces sample and communication complexities in federated Q-learning.
problem Optimal Q-function learning in federated Q-learning with limited communication.
method Introduced Fed-DVR-Q algorithm for order-optimal sample and communication complexities.
result Complete characterization of sample-communication complexity trade-off.
New method finds all Nash equilibria via vector optimization.
problem Finding all Nash equilibria in games.
method Formulate vector optimization problem to find Pareto optimal solutions.
result Characterize set of all Nash equilibria as Pareto optimal solutions.
This paper improves Q-learning bounds using reference-advantage decomposition.
problem Improving Q-learning bounds in MDPs with positive suboptimality gaps.
method Develops a novel error decomposition framework to prove gap-dependent regret bounds.
result Establishes logarithmic gap-dependent regret bounds for Q-learning.
The h-cobordism theorem is a noted theorem in differential and PL topology. A generalization of the h-cobordism theorem for possibly non simply connected manifolds is the so called s-cobordism theorem. In this paper, we prove semialgebraic and Nash versions of these theorems. That is, starting with semialgebraic or Nas…
Study Whittle index learning algorithms for restless bandits with constant stepsizes.
problem Optimizing decisions in restless multi-armed bandits with constant stepsizes.
method Developed Q-learning algorithms with constant stepsizes for index learning in restless bandits, extending to DQN and function approximations.
result The algorithms learn the Whittle index effectively.
Extended analysis of Q-learning's efficiency, matching optimal regret.
problem Theoretical guarantees of Q-learning's efficiency and optimal regret.
method Survey of related research, detailed proof reasoning.
result Q-learning with UCB exploration achieves sample efficiency matching optimal regret.
Proposes a new Q-learning method for survival outcomes in clinical trials.
problem Incomplete follow-up data and nonlinear covariate effects in clinical trials.
method Combines Buckley-James boosting with flexible base learners for estimating optimal treatment regimes.
result Improves treatment decision accuracy and stability in longitudinal clinical trials.
Paper analyzes finite-time convergence of double Q-learning.
problem Overestimation issue in Q-learning.
method Finite-time analysis of double Q-learning.
result Convergence to ε-accurate neighborhood in finite iterations.
A novel Q-learning variant reduces underestimation bias in deep actor-critic methods for reinforcement learning.
problem Underestimation bias in deep actor-critic methods for reinforcement learning.
method Introduces a parameter-free Q-learning variant that combines maximum and minimum operators to bound value estimates.
result Improves state-of-the-art performance on OpenAI Gym tasks.
Robust Q-learning for mean-field control under Wasserstein uncertainty
problem Mean-field control under Wasserstein uncertainty
method Quantization-and-projection scheme with Wasserstein dual reformulation
result Convergence and finite-time iteration bounds
Q-learning is one of the most popular methods in Reinforcement Learning (RL). Transfer Learning aims to utilize the learned knowledge from source tasks to help new tasks to improve the sample complexity of the new tasks. Considering that data collection in RL is both more time and cost consuming and Q-learning converge…
This paper introduces sample-averaged Q-learning for better RL performance.
problem Improving reinforcement learning algorithms by managing uncertainty.
method Integrates statistical inference into Q-learning through sample averaging and functional central limit theorem.
result Establishes a unified theoretical foundation for sample-averaged Q-learning.
Improved sample complexity for target Q-learning in finite MDPs with generative oracle.
problem Sample complexity of target Q-learning in finite MDPs with a generative oracle.
method Analyzed target Q-learning algorithm in tabular case with a generative oracle, improved sample complexity.
result Improved sample complexity for target Q-learning in various scenarios.
Proposes a robust Q-learning method to improve treatment strategy estimation.
problem Misspecification of working models in Q-learning leads to confounding and efficiency loss.
method Uses data-adaptive techniques to estimate nuisance parameters robustly.
result Asymptotic behavior of robust Q-learning estimators is studied and shown to be useful.
Proposes a deep spectral Q-learning for mobile health data.
problem Personalized treatment assignment for patients with time-varying covariates.
method Integrates PCA with deep Q-learning for mixed frequency data.
result Mean return converges to optimal under estimated optimal policy.