In this paper,we propose aprobabilisticmeta-learning algorithm that can sample models for a new task from a modeldistribution.

Thecorrespondingfm (x) where means element-wise Rn.

To extend this and adapt other results to our setting, we could now apply the Simulation Lemma [1]to bound the value difference given the model error,or alternatively, develop the theory in the direction of[55]andrelated work. Code is available at https://github.com/spitis/mocoda Forexample, in2d Navigation,themaskfunction was implementedasfollows: def Mask2dNavigation(input_tensor): """ accepts B x num_sa_features, and returns B x num_parents x num_children """ # base local mask mask = torch.tensor( Theadvantageofthisapproach isthat we can easily do conditional sampling incase of overlapping parent sets. The CQL implementation uses SAC [17].

For regression, we model output noise as a zero-mean Gaussian: N(0,σ2) where σ2 is the varianceofthenoise,treatedasahyperparameter. Neal[21] shows that in the regression setting, the isotropic Gaussian prior for a BNN with a single hidden layer approaches aGaussian process prior asthe number ofhidden units tends toinfinity,solong as the chosen activation function is bounded. We will use this prior in the baseline BNN for our experiments. In the context of BNNs, our Markov chain is a sequence ofrandomparametersW(1),W(2),... definedoverW,whichweconstruct bydefining thetransitionkernel. BBB is scalable and fast, and therefore can be applied to high-dimensional and large datasets in real-life applications.

The ability to encode informative functional beliefs in BNN priors can significantly reduce the bias and uncertainty of the posterior predictive, especially in regions of input space sparsely coveredbytraining data[27].

For each word, we use WordNet [7] to find its synonyms and build a list of word sets. Inaddition, toavoidreplacement clash, wedonotallowanyword to appear in more than word set. Eventually, top 50 semantically matching pairs are retained for CATER. Since the training data of the victim model is unknown to the malicious users, we randomly select 5M sentences from common crawl data as thebenigncorpus. Numbers in parentheses are resultsofcleandata.

We then investigate in detail two adaptivelearning rates-anidealized exactlinesearch andAdaGrad-Norm -on the least squares problem.

This led tothe derivation ofamore general (and involved) characterization of the estimator ˆf. We recall that the distributionπ samples the two datasets according to the process described in Section 2, namely by first samplingρ a task-distribution (onX Y) from µ and then obtaining Dtr and Dval by independently sampling points(x,y) from ρ. Therforeπ = πµ can be seen as implicitlyinducedby µ. The loss4isoftheform(A.5)and admits derivatives ofany order,namely4 C (Z Y X). Assumption 2. Assume Θ Rd1 and D Rd2 compact sets satisfying the cone condition and assume that there exists a reproducing kernelk: D D R with associated RKHSF and s>(d1+2d2)/2suchthatthefunctiong:D HwithH=Ws,2(Θ D),characterizedby g (Dtr)= Z 4(,Dval|)dπ(Dval|Dtr) Dtr D, (A.7) is such that g H F and, for any D D, we have that the application of the operator T(g):F Htothefunctionk(D,) F issuchthatT(g)k(D,)=g (D). The functiong in (A.7) can be interpreted as capturing the interaction between4and the metadistributionπ.

Treatment individualization and adaptation over time are crucial for managing chronic diseases.