5,036 research outputs found
Optimization frameworks and sensitivity analysis of Stackelberg mean-field games
This paper proposes and studies a class of discrete-time finite-time-horizon
Stackelberg mean-field games, with one leader and an infinite number of
identical and indistinguishable followers. In this game, the objective of the
leader is to maximize her reward considering the worst-case cost over all
possible -Nash equilibria among followers. A new analytical paradigm
is established by showing the equivalence between this Stackelberg mean-field
game and a minimax optimization problem. This optimization framework
facilitates studying both analytically and numerically the set of Nash
equilibria for the game; and leads to the sensitivity and the robustness
analysis of the game value. In particular, when there is model uncertainty, the
game value for the leader suffers non-vanishing sub-optimality as the perturbed
model converges to the true model. In order to obtain a near-optimal solution,
the leader needs to be more pessimistic with anticipation of model errors and
adopts a relaxed version of the original Stackelberg game
Linear Quadratic Reinforcement Learning: Sublinear Regret in the Episodic Continuous-Time Framework
In this paper we study a continuous-time linear quadratic reinforcement
learning problem in an episodic setting. We first show that na\"ive
discretization and piecewise approximation with discrete-time RL algorithms
yields a linear regret with respect to the number of learning episodes . We
then propose an algorithm with continuous-time controls based on a regularized
least-squares estimation, and establish a sublinear regret bound in the order
of . The analysis consists of two parts: parameter
estimation error, which relies on properties of sub-exponential random
variables and double stochastic integrals; and perturbation analysis, which
establishes the robustness of the associated continuous-time Riccati equation
by exploiting its regularity property.Comment: 25 page
0- qubit in one Josephson junction
Quantum states are usually fragile which makes quantum computation being not
as stable as classical computation. Quantum correction codes can protect
quantum states but need a large number of physical qubits to code a single
logic qubit. Alternatively, the protection at the hardware level has been
recently developed to maintain the coherence of the quantum information by
using symmetries. However, it generally has to pay the expense of increasing
the complexity of the quantum devices. In this work, we show that the
protection at the hardware level can be approached without increasing the
complexity of the devices. The interplay between the spin-orbit coupling and
the Zeeman splitting in the semiconductor allows us to tune the Josephson
coupling in terms of the spin degree of freedom of Cooper pairs, the hallmark
of the superconducting spintronics. This leads to the implementation of the
parity-protected 0- superconducting qubit with only one highly transparent
superconductor-semiconductor Josephson junction, which makes our proposal
immune from the various fabrication imperfections.Comment: 5 pages, 4 figure
A General Framework for Learning Mean-Field Games
This paper presents a general mean-field game (GMFG) framework for
simultaneous learning and decision-making in stochastic games with a large
population. It first establishes the existence of a unique Nash Equilibrium to
this GMFG, and demonstrates that naively combining reinforcement learning with
the fixed-point approach in classical MFGs yields unstable algorithms. It then
proposes value-based and policy-based reinforcement learning algorithms (GMF-V
and GMF-P, respectively) with smoothed policies, with analysis of their
convergence properties and computational complexities. Experiments on an
equilibrium product pricing problem demonstrate that GMF-V-Q and GMF-P-TRPO,
two specific instantiations of GMF-V and GMF-P, respectively, with Q-learning
and TRPO, are both efficient and robust in the GMFG setting. Moreover, their
performance is superior in convergence speed, accuracy, and stability when
compared with existing algorithms for multi-agent reinforcement learning in the
-player setting.Comment: 43 pages, 7 figures. arXiv admin note: substantial text overlap with
arXiv:1901.0958
Violations of the weak cosmic censorship conjecture in the higher dimensional black holes with pressure
We adopt the energy momentum relation of charged particles to study the
thermodynamics laws and weak cosmic censorship conjecture of -dimensional
AdS black holes in different phase spaces by considering charged
particle absorption. In the normal phase space, it turns out that the laws of
thermodynamic and the weak cosmic censorship conjecture are valid. In the
extended phase space, though the first law of thermodynamics is valid, the
second law of thermodynamics is invalid. More interestingly, the weak cosmic
censorship conjecture is shown to be violated only in higher-dimensional
near-extremal AdS black holes. In addition, the magnitudes of the
violations for both the second law and weak cosmic censorship conjecture are
dependent on the charge , constant scalar curvature , AdS radius
, dimension parameters , and their variations.Comment: Accepted by Eur. Phys. J.
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