Almost Linearity T argeting, based on medium-scale almost linearity assumptions.

We adopt the natural assumption that the empirical NTK develops a block structure aligned with the class labels, i.e., samples within the same class have stronger

Theoptimalbaseline, however, israrelyusedinpractice (Sutton & Barto (2018); foran exception, see (Peters & Schaal, 2008)). Equation (1) thentakesthefollowingform: r E R(x)= E (R(x) B)r log (x).

Ourmethodologyincorporates a certain amount of backtracking when needed, allowing changes in causally preceding variables tominimize deviations from realistic scenarios. Specifically, we introduce a novel optimization framework that permits but also controls the extent of backtracking with a "naturalness" criterion. Empirical experiments demonstrate the effectiveness of our method.

Conformal prediction (CP) is a general framework to quantify the predictive uncertainty of machine learning models that uses a set prediction to include the true label with a valid probability. To align the uncertainty measured by CP, confor-mal training methods minimize the size of the prediction sets. A typical way is to use a surrogate indicator function, usually Sigmoid or Gaussian error function. However, these surrogate functions do not have a uniform error bound to the indicator function, leading to uncontrollable learning bounds. In this paper, we propose a simple cost-sensitive conformal training algorithm that does not rely on the indicator approximation mechanism. Specifically, we theoretically show that minimizing the expected size of prediction sets is upper bounded by the expected rank of true labels. To this end, we develop a rank weighting strategy that assigns the weight using the rank of true label on each data sample. Our analysis provably demonstrates the tightness between the proposed weighted objective and the expected size of conformal prediction sets. Extensive experiments verify the validity of our theoretical insights, and superior empirical performance over other con-formal training in terms of predictive efficiency with 21.38% reduction for average prediction set size.

This paper investigates simple bilevel optimization problems where we minimize an upper-level objective over the optimal solution set of a convex lower-level objective. Existing methods for such problems either only guarantee asymptotic convergence, have slow sublinear rates, or require strong assumptions. To address these challenges, we propose a penalization framework that delineates the relationship between approximate solutions of the original problem and its reformulated counterparts.

Almost Linearity T argeting, based on medium-scale almost linearity assumptions.