Despite this, q-means is still useful for machine learning purposes.

We show the superior performance of our methods in sparsity-inducing constrained optimization, notably Google's personalized

Deep learning models are increasingly popular in many machine learning applications where the training data may contain sensitive information. To provide formal and rigorous privacy guarantee, many learning systems now incorporate differential privacy by training their models with (differentially) private SGD.

We thank the reviewers for their positive and constructive feedback. We address several points in the review below. The bias reduction technique in Section 5 is designed for DP-SGD with clipping. Section 5, the results are similar to thoise in the figure in Section 5 (which used σ = 0 for all algorithms). Typos: Thank you for pointing them out, we will correct the typos.

Subspace learning is a critical endeavor in contemporary machine learning, particularly given the vast dimensions of modern datasets.

Offline reinforcement learning (RL) can be used to improve future performance by leveraging historical data. There exist many different algorithms for offline RL, and it is well recognized that these algorithms, and their hyperparameter settings, can lead to decision policies with substantially differing performance. This prompts the need for pipelines that allow practitioners to systematically perform algorithmhyperparameter selection for their setting. Critically, in most real-world settings, this pipeline must only involve the use of historical data. Inspired by statistical model selection methods for supervised learning, we introduce a task-and methodagnostic pipeline for automatically training, comparing, selecting, and deploying the best policy when the provided dataset is limited in size.

Recent methodologies in LLM self-training mostly rely on LLM generating responses and filtering those with correct output answers as training data. This approach often yields a low-quality fine-tuning training set (e.g., incorrect plans or intermediate reasoning).

The most prevalent approach for estimating endogenous regression models with instruments is assuming low-dimensional linear relationships, i.e. h The coefficient in the final regression is taken to be the estimate of . Then a 2SLS estimation method is applied on these transformed feature spaces. The authors show asymptotic consistency of the resulting estimator, assuming that the approximation error goes to zero. Subsequently, they also estimate the function m(z) =E[y h(x) | z] based on another growing sieve. Though it may seem at first that the approach in that paper and ours are quite distinct, the population limit of our objective function coincides with theirs. To see this, consider the simplified version of our estimator presented in (6), where the function classes are already norm-constrained and no norm based regularization is imposed. Moreover, for a moment consider the population version of this estimator, i.e. min max (h, f) kfk Thus in the population limit and without norm regularization on the test function f, our criterion is equivalent to the minimum distance criterion analyzed in Chen and Pouzo [2012]. Another point of similarity is that we prove convergence of the estimator in terms of the pseudo-metric, the projected MSE defined in Section 4 of Chen and Pouzo [2012] - and like that paper we require additional conditions to relate the pseudo-metric to the true MSE. The present paper differs in a number of ways: (i) the finite sample criterion is different; (ii) we prove our results using localized Rademacher analysis which allows for weaker assumptions; (iii) we consider a broader range of estimation approaches than linear sieves, necessitating more of a focus on optimization. Digging into the second point, Chen and Pouzo [2012] take a more traditional parameter recovery approach which requires several minimum eigenvalue conditions and several regularity conditions to be satisfied for their estimation rate to hold (see e.g. This is analogous to a mean squared error proof in an exogenous linear regression setting, that requires the minimum eigenvalue of the feature co-variance to be bounded away from zero. Moreover, such parameter recovery methods seem limited to the growing sieve approach, since only then one has a clear finite dimensional parameter vector to work on for each fixed n.

Recent Reinforcement Learning (RL) algorithms making use of Kullback-Leibler (KL) regularization as a core component have shown outstanding performance. Yet, only little is understood theoretically about why KL regularization helps, so far. We study KL regularization within an approximate value iteration scheme and show that it implicitly averages q-values. Leveraging this insight, we provide a very strong performance bound, the very first to combine two desirable aspects: a linear dependency to the horizon (instead of quadratic) and an error propagation term involving an averaging e ect of the estimation errors (instead of an accumulation e ect). We also study the more general case of an additional entropy regularizer. The resulting abstract scheme encompasses many existing RL algorithms. Some of our assumptions do not hold with neural networks, so we complement this theoretical analysis with an extensive empirical study.

Generic motion understanding from video involves not only tracking objects, but also perceiving how their surfaces deform and move. This information is useful to make inferences about 3D shape, physical properties and object interactions. While the problem of tracking arbitrary physical points on surfaces over longer video clips has received some attention, no dataset or benchmark for evaluation existed, until now.