3,245 research outputs found
The Extended Regularized Dual Averaging Method for Composite Optimization
We present a new algorithm, extended regularized dual averaging (XRDA), for
solving composite optimization problems, which are a generalization of the
regularized dual averaging (RDA) method. The main novelty of the method is that
it allows more flexible control of the backward step size. For instance, the
backward step size for RDA grows without bound, while XRDA the backward step
size can be kept bounded
Echoes of chaos from string theory black holes
The strongly coupled D1-D5 conformal field theory is a microscopic model of
black holes which is expected to have chaotic dynamics. Here, we study the weak
coupling limit of the theory where it is integrable rather than chaotic. In
this limit, the operators creating microstates of the lowest mass black hole
are known exactly. We consider the time-ordered two-point function of light
probes in these microstates, normalized by the same two-point function in
vacuum. These correlators display a universal early-time decay followed by
late-time sporadic behavior. To find a prescription for temporal
coarse-graining of these late fluctuations we appeal to random matrix theory,
where we show that a progressive time-average smooths the spectral form factor
(a proxy for the 2-point function) in a typical draw of a random matrix. This
coarse-grained quantity reproduces the matrix ensemble average to a good
approximation. Employing this coarse-graining in the D1-D5 system, we find that
the early-time decay is followed by a dip, a ramp and a plateau, in remarkable
qualitative agreement with recent studies of the Sachdev-Ye-Kitaev (SYK) model.
We study the timescales involved, comment on similarities and differences
between our integrable model and the chaotic SYK model, and suggest ways to
extend our results away from the integrable limit.Comment: 26 pages, 9 figures, v3: discussion of dip time adde
Online Convex Optimization for Sequential Decision Processes and Extensive-Form Games
Regret minimization is a powerful tool for solving large-scale extensive-form
games. State-of-the-art methods rely on minimizing regret locally at each
decision point. In this work we derive a new framework for regret minimization
on sequential decision problems and extensive-form games with general compact
convex sets at each decision point and general convex losses, as opposed to
prior work which has been for simplex decision points and linear losses. We
call our framework laminar regret decomposition. It generalizes the CFR
algorithm to this more general setting. Furthermore, our framework enables a
new proof of CFR even in the known setting, which is derived from a perspective
of decomposing polytope regret, thereby leading to an arguably simpler
interpretation of the algorithm. Our generalization to convex compact sets and
convex losses allows us to develop new algorithms for several problems:
regularized sequential decision making, regularized Nash equilibria in
extensive-form games, and computing approximate extensive-form perfect
equilibria. Our generalization also leads to the first regret-minimization
algorithm for computing reduced-normal-form quantal response equilibria based
on minimizing local regrets. Experiments show that our framework leads to
algorithms that scale at a rate comparable to the fastest variants of
counterfactual regret minimization for computing Nash equilibrium, and
therefore our approach leads to the first algorithm for computing quantal
response equilibria in extremely large games. Finally we show that our
framework enables a new kind of scalable opponent exploitation approach
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