The high-level architecture of our simulator is illustrated in Figure 1 of Section 4. Additional details (with references to objects in the source code) are provided below. Simulations were run in Python 3.8 on an Intel(R) Xeon(R) CPU E5-2667 One direction is to extend the feature description of the ads (beyond topic) to include features that reflect ad quality and location. Baseline parameters are: µ = 0 . The resulting cohort errors are consistent with Figure 1 of Section 5.1. For the fully informative prior, the agent is completely certain of users' cohorts for Lastly, for the uninformative prior, revelation of a user's cookie does not inform the The agent's ability to distinguish users based on their responses depends on the similarities of affinities across users in different cohorts.

The classical optimal transport (OT) problem seeks the map that moves mass from a source to a target measure while minimizing a prescribed cost function. The objective can be formalized in either Monge's [12] or Kantronich's formulation [10], a convex relaxation of the former that considers transport plans instead of deterministic maps. These foundational formulations have wide-ranging applications, including to economics [7] and machine learning [14]. In many practical scenarios, the source measure is known or readily in-ferrable from empirical data but the target measure is not explicitly specified. Instead, it is only constrained by practical requirements or expert knowledge. For example, when applying Monge's formulation to transportation problems, the placement of the mass in the target region may be constrained to lie entirely beyond a certain boundary or within a particular region, rather than by the specification of a precise location for each fraction of the total mass. Similarly, in economic applications, supply and demand may be subject to constraints such as maximal amounts available or minimal amounts required, rather than dictated through precise marginal distributions. 1

We consider a discrete-time formulation for a class of high-dimensional stochastic joint replenishment problems. First, we approximate the problem by a continuous-time impulse control problem. Exploiting connections among the impulse control problem, backward stochastic differential equations (BSDEs) with jumps, and the stochastic target problem, we develop a novel, simulation-based computational method that relies on deep neural networks to solve the impulse control problem. Based on that solution, we propose an implementable inventory control policy for the original (discrete-time) stochastic joint replenishment problem, and test it against the best available benchmarks in a series of test problems. For the problems studied thus far, our method matches or beats the best benchmark we could find, and it is computationally feasible up to at least 50 dimensions -- that is, 50 stock-keeping units (SKUs).

Slutsky's theorem together with (S.3) and (S.5) implies the result in Theorem 1. Now we check the Lindeberg-Feller condition. 's are non-negative and E S.4 Derivation of corrected model (4) Note that π (x, 1) = 1 and π (x, 0) = π (x) . Slutsky's theorem together with (S.15) and (S.17) implies the result in Theorem 1. 's, whose distribution depends on N . From (S.27) and (S.28), Chebyshev's inequality implies that For sampled data, (5) tell us that the joint density w.r.t. the product counting measure of the responses The outline of the proof is similar to that of the proof of Theorem 2. Write Markov's inequality shows that they are both o The outline of the proof is similar to that of the proof of Theorem 4. The estimator Slutsky's theorem together with (S.38) and (S.40) implies the result in Theorem 1.

Most current models use deterministic attention modules due to their simplicity and ease of optimization. Stochastic counterparts, on the other hand, are less popular despite their potential benefits.

Large image generation and vision models, combined with differentiable rendering technologies, have become powerful tools for generating paths that can be drawn or painted by a robot. However, these tools often overlook the intrinsic physicality of the human drawing/writing act, which is usually executed with skillful hand/arm gestures. Taking this into account is important for the visual aesthetics of the results and for the development of closer and more intuitive artist-robot collaboration scenarios. We present a method that bridges this gap by enabling gradient-based optimization of natural human-like motions guided by cost functions defined in image space. To this end, we use the sigma-lognormal model of human hand/arm movements, with an adaptation that enables its use in conjunction with a differentiable vector graphics (DiffVG) renderer. We demonstrate how this pipeline can be used to generate feasible trajectories for a robot by combining image-driven objectives with a minimum-time smoothing criterion. We demonstrate applications with generation and robotic reproduction of synthetic graffiti as well as image abstraction.

A growing trend in the database and system communities is to augment conventional index structures, such as B+-trees, with machine learning (ML) models. Among these, error-bounded Piecewise Linear Approximation ($ε$-PLA) has emerged as a popular choice due to its simplicity and effectiveness. Despite its central role in many learned indexes, the design and analysis of $ε$-PLA fitting algorithms remain underexplored. In this paper, we revisit $ε$-PLA from both theoretical and empirical perspectives, with a focus on its application in learned index structures. We first establish a fundamentally improved lower bound of $Ω(κ\cdot ε^2)$ on the expected segment coverage for existing $ε$-PLA fitting algorithms, where $κ$ is a data-dependent constant. We then present a comprehensive benchmark of state-of-the-art $ε$-PLA algorithms when used in different learned data structures. Our results highlight key trade-offs among model accuracy, model size, and query performance, providing actionable guidelines for the principled design of future learned data structures.