1,426 research outputs found
Entropy-Regularized Stochastic Games
In two-player zero-sum stochastic games, where two competing players make
decisions under uncertainty, a pair of optimal strategies is traditionally
described by Nash equilibrium and computed under the assumption that the
players have perfect information about the stochastic transition model of the
environment. However, implementing such strategies may make the players
vulnerable to unforeseen changes in the environment. In this paper, we
introduce entropy-regularized stochastic games where each player aims to
maximize the causal entropy of its strategy in addition to its expected payoff.
The regularization term balances each player's rationality with its belief
about the level of misinformation about the transition model. We consider both
entropy-regularized -stage and entropy-regularized discounted stochastic
games, and establish the existence of a value in both games. Moreover, we prove
the sufficiency of Markovian and stationary mixed strategies to attain the
value, respectively, in -stage and discounted games. Finally, we present
algorithms, which are based on convex optimization problems, to compute the
optimal strategies. In a numerical example, we demonstrate the proposed method
on a motion planning scenario and illustrate the effect of the regularization
term on the expected payoff.Comment: Corrected typo
Entropy-Regularized Stochastic Games
In zero-sum stochastic games, where two competing players make decisions under uncertainty, a pair of optimal strategies is traditionally described by Nash equilibrium and computed under the assumption that the players have perfect information about the stochastic transition model of the environment. However, implementing such strategies may make the players vulnerable to unforeseen changes in the environment. In this paper, we introduce entropy-regularized stochastic games where each player aims to maximize the causal entropy of its strategy in addition to its expected payoff. The regularization term balances each player's rationality with its belief about the level of misinformation about the transition model. We consider both entropy-regularized N-stage and entropy-regularized discounted stochastic games, and establish the existence of a value in both games. Moreover, we prove the sufficiency of Markovian and stationary mixed strategies to attain the value, respectively, in N-stage and discounted games. Finally, we present algorithms, which are based on convex optimization problems, to compute the optimal strategies. In a numerical example, we demonstrate the proposed method on a motion planning scenario and illustrate the effect of the regularization term on the expected payoff
A Theory of Regularized Markov Decision Processes
Many recent successful (deep) reinforcement learning algorithms make use of
regularization, generally based on entropy or Kullback-Leibler divergence. We
propose a general theory of regularized Markov Decision Processes that
generalizes these approaches in two directions: we consider a larger class of
regularizers, and we consider the general modified policy iteration approach,
encompassing both policy iteration and value iteration. The core building
blocks of this theory are a notion of regularized Bellman operator and the
Legendre-Fenchel transform, a classical tool of convex optimization. This
approach allows for error propagation analyses of general algorithmic schemes
of which (possibly variants of) classical algorithms such as Trust Region
Policy Optimization, Soft Q-learning, Stochastic Actor Critic or Dynamic Policy
Programming are special cases. This also draws connections to proximal convex
optimization, especially to Mirror Descent.Comment: ICML 201
A Regularized Opponent Model with Maximum Entropy Objective
In a single-agent setting, reinforcement learning (RL) tasks can be cast into
an inference problem by introducing a binary random variable o, which stands
for the "optimality". In this paper, we redefine the binary random variable o
in multi-agent setting and formalize multi-agent reinforcement learning (MARL)
as probabilistic inference. We derive a variational lower bound of the
likelihood of achieving the optimality and name it as Regularized Opponent
Model with Maximum Entropy Objective (ROMMEO). From ROMMEO, we present a novel
perspective on opponent modeling and show how it can improve the performance of
training agents theoretically and empirically in cooperative games. To optimize
ROMMEO, we first introduce a tabular Q-iteration method ROMMEO-Q with proof of
convergence. We extend the exact algorithm to complex environments by proposing
an approximate version, ROMMEO-AC. We evaluate these two algorithms on the
challenging iterated matrix game and differential game respectively and show
that they can outperform strong MARL baselines.Comment: Accepted to International Joint Conference on Artificial Intelligence
(IJCA2019
Distral: Robust Multitask Reinforcement Learning
Most deep reinforcement learning algorithms are data inefficient in complex
and rich environments, limiting their applicability to many scenarios. One
direction for improving data efficiency is multitask learning with shared
neural network parameters, where efficiency may be improved through transfer
across related tasks. In practice, however, this is not usually observed,
because gradients from different tasks can interfere negatively, making
learning unstable and sometimes even less data efficient. Another issue is the
different reward schemes between tasks, which can easily lead to one task
dominating the learning of a shared model. We propose a new approach for joint
training of multiple tasks, which we refer to as Distral (Distill & transfer
learning). Instead of sharing parameters between the different workers, we
propose to share a "distilled" policy that captures common behaviour across
tasks. Each worker is trained to solve its own task while constrained to stay
close to the shared policy, while the shared policy is trained by distillation
to be the centroid of all task policies. Both aspects of the learning process
are derived by optimizing a joint objective function. We show that our approach
supports efficient transfer on complex 3D environments, outperforming several
related methods. Moreover, the proposed learning process is more robust and
more stable---attributes that are critical in deep reinforcement learning
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