The LifeTime Value (LTV) prediction, which endeavors to forecast the cumulative purchase contribution of a user to a particular item, remains a vital challenge that advertisers are keen to resolve. A precise LTV prediction system enhances the alignment of user interests with meticulously designed advertisements, thereby generating substantial profits for advertisers. Nonetheless, this issue is complicated by the paucity of data typically observed in real-world advertising scenarios. The purchase rate among registered users is often as critically low as 0.1%, resulting in a dataset where the majority of users make only several purchases. Consequently, there is insufficient supervisory signal for effectively training the LTV prediction model. An additional challenge emerges from the interdependencies among tasks with high correlation. It is a common practice to estimate a user's contribution to a game over a specified temporal interval. Varying the lengths of these intervals corresponds to distinct predictive tasks, which are highly correlated. For instance, predictions over a 7-day period are heavily reliant on forecasts made over a 3-day period, where exceptional cases can adversely affect the accuracy of both tasks. In order to comprehensively address the aforementioned challenges, we introduce an innovative framework denoted as Graph-Represented Pareto-Optimal LifeTime Value prediction (GRePO-LTV). Graph representation learning is initially employed to address the issue of data scarcity. Subsequently, Pareto-Optimization is utilized to manage the interdependence of prediction tasks.

Selecting the optimal subset from a large set of variables is a fundamental problem in various learning tasks such as feature selection, sparse regression, dictionary learning, etc. In this paper, we propose the POSS approach which employs evolutionary Pareto optimization to find a small-sized subset with good performance. We prove that for sparse regression, POSS is able to achieve the best-so-far theoretically guaranteed approximation performance efficiently. Particularly, for the \emph{Exponential Decay} subclass, POSS is proven to achieve an optimal solution. Empirical study verifies the theoretical results, and exhibits the superior performance of POSS to greedy and convex relaxation methods.

Existing music generation models are mostly language-based, neglecting the frequency continuity property of notes, resulting in inadequate fitting of rare or never-used notes and thus reducing the diversity of generated samples. We argue that the distribution of notes can be modeled by translational invariance and periodicity, especially using diffusion models to generalize notes by injecting frequency-domain Gaussian noise. However, due to the low-density nature of music symbols, estimating the distribution of notes latent in the high-density solution space poses significant challenges. To address this problem, we introduce the Music-Diff architecture, which fits a joint distribution of notes and accompanying semantic information to generate symbolic music conditionally. We first enhance the fragmentation module for extracting semantics by using event-based notations and the structural similarity index, thereby preventing boundary blurring. As a prerequisite for multivariate perturbation, we introduce a joint pre-training method to construct the progressions between notes and musical semantics while avoiding direct modeling of low-density notes. Finally, we recover the perturbed notes by a multi-branch denoiser that fits multiple noise objectives via Pareto optimization. Our experiments suggest that in contrast to language models, joint probability diffusion models perturbing at both note and semantic levels can provide more sample diversity and compositional regularity. The case study highlights the rhythmic advantages of our model over language- and DDPMs-based models by analyzing the hierarchical structure expressed in the self-similarity metrics.

Optimization of accelerator performance parameters is limited by numerous trade-offs and finding the appropriate balance between optimization goals for an unknown system is challenging to achieve. Here we show that multi-objective Bayesian optimization can map the solution space of a laser wakefield accelerator in a very sample-efficient way. Using a Gaussian mixture model, we isolate contributions related to an electron bunch at a certain energy and we observe that there exists a wide range of Pareto-optimal solutions that trade beam energy versus charge at similar laser-to-beam efficiency. However, many applications such as light sources require particle beams at a certain target energy. Once such a constraint is introduced we observe a direct trade-off between energy spread and accelerator efficiency. We furthermore demonstrate how specific solutions can be exploited using \emph{a posteriori} scalarization of the objectives, thereby efficiently splitting the exploration and exploitation phases.

Pareto optimization solves a constrained optimization task by reformulating the task as a bi-objective problem. Pareto optimization has been shown quite effective in applications; however, it has little theoretical support. This work theoretically compares Pareto optimization with a penalty approach, which is a common method transforming a constrained optimization into an unconstrained optimization. We prove that on two large classes of constrained Boolean optimization problems, minimum matroid optimization (P-solvable) and minimum cost coverage (NP-hard), Pareto optimization is more efficient than the penalty function method for obtaining the optimal and approximate solutions, respectively. Furthermore, on a minimum cost coverage instance, we also show the advantage of Pareto optimization over a greedy algorithm.

About a year ago, I wrote an article introducing the concept of optimizing road trips using a combination of genetic algorithms and Google Maps. During that time, I've given some thought to how I could make that algorithm more useful to folks looking to plan their summer road trips. One thought that struck me was that the road trips I created before were quite grandiose--spanning entire states or even most of Europe--such that only people who had some savings and were able to take a month off of work could even hope to go on one of the trips. In reality, most of us have budgetary constraints on our road trips: we can only spend so much money, or we only have so much time off before we have to get back to work. In this article, I'm going to expand on the idea of optimizing road trips by introducing multi-objective Pareto optimization to the algorithm.

Pareto optimization solves a constrained optimization task by reformulating the task as a bi-objective problem. Pareto optimization has been shown quite effective in applications; however, it has little theoretical support. This work theoretically compares Pareto optimization with a penalty approach, which is a common method transforming a constrained optimization into an unconstrained optimization. We prove that on two large classes of constrained Boolean optimization problems, minimum matroid optimization (P-solvable) and minimum cost coverage (NP-hard), Pareto optimization is more efficient than the penalty function method for obtaining the optimal and approximate solutions, respectively. Furthermore, on a minimum cost coverage instance, we also show the advantage of Pareto optimization over a greedy algorithm.