While therewardcompensation mechanism isunknown,the learner can adapt his (her) decision to the past reward feedback so as to maximize the sum of rewards.

We show in this paper that all existing implementations of gradient boosting face the following statistical issue.

FedAvg: FedAvg [29] has become a de facto standard federated learning algorithm in practice. However,it has several limitations as discussed in many papers, including [23]. It is also difficult to analyze convergence of FedAvg, especially in the nonconvex case andheterogeneity settings (both statistical andsystem heterogeneity). Moreover,FedAvg originally specifies SGD with a fixed number of epochs and a fixed learning rate as its local solver,making itlessflexible inpractice.

Somewhat surprisingly, learning in a Markov Decision Process is most often considered under the performance criteria ofconsistency or regret minimization(see e.g.

Similarly the ISOMAP face database consists ofimages (256levels ofgray)ofsize64 64,i.e.,vectors in R4096, whereas the correct intrinsic dimension is only3 (for the vertical, horizontal pause and lightingdirection). The second approach, is anaverage caseapproach (in the spirit of thestatistical mechanics treatment ofhighdimensional systems), thatmodelsfeaturevectorsby arandom ensemble,taken as aset ofrandom vectors with independently identically distributed (i.i.d.) components, and a small but xed fraction of non-zero components.

Thistask is challenging because the causal graph is unknown and even there may exist latent confounders.

Moreover,tofurther accelerate overgreedy descent methods, wepresent a new accelerated random search (ARS) algorithm that incorporates prior information, together with aconvergence analysis.

LetT be the time horizon andPT be the path-length that essentially reflects the non-stationarity of environments, the state-of-the-art dynamicregretis O( p T(1+PT)).

Several popularly used FL algorithms for this setting includeFedAvg (McMahan et al., 2017), FedProx(Lietal.,2020b), We analyze its convergence behavior, expose problems, andpropose alternativesmore suitable forscaling upandgeneralization.

We study the Bayesian regret of the renowned Thompson Sampling algorithm incontextual bandits with binary losses and adversarially-selected contexts.