161 research outputs found
Universal Learning of Repeated Matrix Games
We study and compare the learning dynamics of two universal learning
algorithms, one based on Bayesian learning and the other on prediction with
expert advice. Both approaches have strong asymptotic performance guarantees.
When confronted with the task of finding good long-term strategies in repeated
2x2 matrix games, they behave quite differently.Comment: 16 LaTeX pages, 8 eps figure
Asymptotics of Discrete MDL for Online Prediction
Minimum Description Length (MDL) is an important principle for induction and
prediction, with strong relations to optimal Bayesian learning. This paper
deals with learning non-i.i.d. processes by means of two-part MDL, where the
underlying model class is countable. We consider the online learning framework,
i.e. observations come in one by one, and the predictor is allowed to update
his state of mind after each time step. We identify two ways of predicting by
MDL for this setup, namely a static} and a dynamic one. (A third variant,
hybrid MDL, will turn out inferior.) We will prove that under the only
assumption that the data is generated by a distribution contained in the model
class, the MDL predictions converge to the true values almost surely. This is
accomplished by proving finite bounds on the quadratic, the Hellinger, and the
Kullback-Leibler loss of the MDL learner, which are however exponentially worse
than for Bayesian prediction. We demonstrate that these bounds are sharp, even
for model classes containing only Bernoulli distributions. We show how these
bounds imply regret bounds for arbitrary loss functions. Our results apply to a
wide range of setups, namely sequence prediction, pattern classification,
regression, and universal induction in the sense of Algorithmic Information
Theory among others.Comment: 34 page
Adaptive Online Prediction by Following the Perturbed Leader
When applying aggregating strategies to Prediction with Expert Advice, the
learning rate must be adaptively tuned. The natural choice of
sqrt(complexity/current loss) renders the analysis of Weighted Majority
derivatives quite complicated. In particular, for arbitrary weights there have
been no results proven so far. The analysis of the alternative "Follow the
Perturbed Leader" (FPL) algorithm from Kalai & Vempala (2003) (based on
Hannan's algorithm) is easier. We derive loss bounds for adaptive learning rate
and both finite expert classes with uniform weights and countable expert
classes with arbitrary weights. For the former setup, our loss bounds match the
best known results so far, while for the latter our results are new.Comment: 25 page
Nonstochastic bandits: Countable decision set, unbounded costs and reactive environments
AbstractThe nonstochastic multi-armed bandit problem, first studied by Auer, Cesa-Bianchi, Freund, and Schapire in 1995, is a game of repeatedly choosing one decision from a set of decisions (“experts”), under partial observation: In each round t, only the cost of the decision played is observable. A regret minimization algorithm plays this game while achieving sublinear regret relative to each decision. It is known that an adversary controlling the costs of the decisions can force the player a regret growing as t12 in the time t. In this work, we propose the first algorithm for a countably infinite set of decisions, that achieves a regret upper bounded by O(t12+ε), i.e. arbitrarily close to optimal order. To this aim, we build on the “follow the perturbed leader” principle, which dates back to work by Hannan in 1957. Our results hold against an adaptive adversary, for both the expected and high probability regret of the learner w.r.t. each decision. In the second part of the paper, we consider reactive problem settings, that is, situations where the learner’s decisions impact on the future behaviour of the adversary, and a strong strategy can draw benefit from well chosen past actions. We present a variant of our regret minimization algorithm which has still regret of order at most t12+ε relative to such strong strategies, and even sublinear regret not exceeding O(t45) w.r.t. the hypothetical (without external interference) performance of a strong strategy. We show how to combine the regret minimizer with a universal class of experts, given by the countable set of programs on some fixed universal Turing machine. This defines a universal learner with sublinear regret relative to any computable strategy
Master algorithms for active experts problems based on increasing loss values
We specify an experts algorithm with the following
characteristics: (a) it uses only feedback from the actions
actually chosen (bandit setup), (b) it can be applied with
countably infinite expert classes, and (c) it copes with
losses that may grow in time appropriately slowly. We
prove loss bounds against an adaptive adversary. From this, we
obtain master algorithms for ``active experts problems'', which
means that the master's actions may influence the behavior of
the adversary. Our algorithm can significantly outperform
standard experts algorithms on such problems. Finally, we
combine it with a universal expert class. This results in a
(computationally infeasible) universal master algorithm
which performs - in a certain sense - almost as well as any
computable strategy, for any online problem
Quantitative real-time imaging of intracellular FRET biosensor dynamics using rapid multi-beam confocal FLIM
Fluorescence lifetime imaging (FLIM) is a quantitative, intensity-independent microscopical method for measurement of diverse biochemical and physical properties in cell biology. It is a highly effective method for measurements of Förster resonance energy transfer (FRET), and for quantification of protein-protein interactions in cells. Time-domain FLIM-FRET measurements of these dynamic interactions are particularly challenging, since the technique requires excellent photon statistics to derive experimental parameters from the complex decay kinetics often observed from fluorophores in living cells. Here we present a new time-domain multi-confocal FLIM instrument with an array of 64 visible beamlets to achieve parallelised excitation and detection with average excitation powers of ~ 1–2 μW per beamlet. We exemplify this instrument with up to 0.5 frames per second time-lapse FLIM measurements of cAMP levels using an Epac-based fluorescent biosensor in live HeLa cells with nanometer spatial and picosecond temporal resolution. We demonstrate the use of time-dependent phasor plots to determine parameterisation for multi-exponential decay fitting to monitor the fractional contribution of the activated conformation of the biosensor. Our parallelised confocal approach avoids having to compromise on speed, noise, accuracy in lifetime measurements and provides powerful means to quantify biochemical dynamics in living cells
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