Keyword Analysis & Research: regret bound

stackexchange.com

https://datascience.stackexchange.com/questions/62141/what-are-regret-bounds

A regret bound measures the performance of an online algorithm relative to the performance of a competing prediction mechanism, called a competing hypothesis." I am still confused after reading this (I did not read the rest of the thesis as it is way above my understanding in that field). Could someone please explain? Many thanks in advance!

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umd.edu

https://www.cs.umd.edu/~slivkins/CMSC858G-fall16/Lecture%205.pdf

a general technique: it can be used to upper-bound Bayesian regret of Thompson Sampling for arbitrary priors, and it also for a particular class of priors (e.g., priors over linear reward functions) whenever one has \nice" con dence bounds Uand Lfor this class. Let us use Lemma 1.1 to prove a O(p KTlogT) upper bound on regret, which matches the File Size: 217KB Page Count: 5

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github.io

https://rl-vs.github.io/rlvs2021/class-material/regret_bounds_model_based_rl/RLVS-Wang-modelRL.pdf

•d is the doubling dimension of s-a space •D is the diameter of s-a space •Theorem The above regret bound is minimax optimal. Regret(K) =O(DLK) d+ d1⋅H (Learn to Control In Metric Space with Optimal Regret, Allerton, 2019. With Ni and Yang.) Doubling Dimension •Here be the doubling dimensionof the state space File Size: 1MB Page Count: 23

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sshekhar.page

https://sshekhar.page/post/uit-mixture-method1/

Jul 08, 2021 · Summary: Derivation of upper bound on the regret for the mixture method (KT scheme) for individual sequence prediction. Suppose X = { 1, …, m } for some integer m ≥ 2 and let Θ = Δ m denote the m − 1 dimensional probability simplex. We will use p θ on X to denote the distribution parametrized by any θ ∈ Θ. Consider the following game.

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wikipedia.org

https://en.wikipedia.org/wiki/Regret_%28decision_theory%29

What follows is an illustration of how the concept of regret can be used to design a linear estimator. In this example, the problem is to construct a linear estimator of a finite-dimensional parameter vector from its noisy linear measurement with known noise covariance structure. The loss of reconstruction of is measured using the mean-squared error (MSE). The unknown parameter vector is known to lie in an ellipsoid centered at zero. The regret is defined to be the difference betwee…

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neurips.cc

https://proceedings.neurips.cc/paper/2018/file/6c1e55ec7c43dc51a37472ddcbd756fb-Paper.pdf

Tables 1 and 2 summarize the regret bounds for the special case in which the cardinality of assets is restricted to be at most 1 or at most k. As shown in Table 1, Algorithm 1 can achieve regret of O( p Tpoly(d)) even if k= (d) when Shas an exponentially large size with respect to d.

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cornell.edu

https://www.cs.cornell.edu/~rdk/papers/colt08.pdf

(In this bound, the big-O hides a constant depending on the means and differ-ences of means of payoffs.) For the adversarial version of the multi-armed bandit problem, Auer, Cesa-Bianchi, Fre-und, and Schapire [ACBFS02] proposed the algorithm Exp3 which achieves the regret bound of O(√ Tnlogn), leaving a √ logn factor gap from the lower ...

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mlr.press

http://proceedings.mlr.press/v70/azar17a/azar17a.pdf

We show that an optimistic modification to value iteration achieves a regret bound of Oe( p HSAT+H2S2A+H p T) where His the time horizon, Sthe number of states, A the number of actions and Tthe number of time- steps. This result improves over the best previ- ous known bound Oe(HS p AT) achieved by the UCRL2 algorithm ofJaksch et al.(2010).

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mit.edu

https://www.mit.edu/~rakhlin/papers/bandit_merged.pdf

For oblivious adversaries, they proved a regret bound of O (poly(n)T2=3). The case of a general adaptive adversary was handled by McMahan and Blum [14] but they could only prove a regret bound of O (poly(n)T3=4). Dani and Hayes [7] later showed that McMahan and Blum’s al- gorithm actually enjoys a regret bound of O (poly(n)T2=3).

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nyu.edu

https://cs.nyu.edu/~mohri/ml/ml09/regret.pdf

Regret Minimization: Algorithms and Applications Yishay Mansour Google & Tel Aviv Univ. Many thanks for my co-authors: A. Blum, N. Cesa-Bianchi, and G. Stoltz. 2. Weather Forecast • Sunny: • Rainy: ... External Regret: Summary • We showed a bound of …

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