In many recent works, the potential of Exploratory Landscape Analysis (ELA) features to numerically characterize, in particular, single-objective continuous optimization problems has been demonstrated. These numerical features provide the input for all kinds of machine learning tasks on continuous optimization problems, ranging, i.a., from High-level Property Prediction to Automated Algorithm Selection and Automated Algorithm Configuration. Without ELA features, analyzing and understanding the characteristics of single-objective continuous optimization problems would be impossible. Yet, despite their undisputed usefulness, ELA features suffer from several drawbacks. These include, in particular, (1.) a strong correlation between multiple features, as well as (2.) its very limited applicability to multi-objective continuous optimization problems. As a remedy, recent works proposed deep learning-based approaches as alternatives to ELA. In these works, e.g., point-cloud transformers were used to characterize an optimization problem's fitness landscape. However, these approaches require a large amount of labeled training data. Within this work, we propose a hybrid approach, Deep-ELA, which combines (the benefits of) deep learning and ELA features. Specifically, we pre-trained four transformers on millions of randomly generated optimization problems to learn deep representations of the landscapes of continuous single- and multi-objective optimization problems. Our proposed framework can either be used out-of-the-box for analyzing single- and multi-objective continuous optimization problems, or subsequently fine-tuned to various tasks focussing on algorithm behavior and problem understanding.

We consider an online two-stage stochastic optimization with long-term constraints over a finite horizon of $T$ periods. At each period, we take the first-stage action, observe a model parameter realization and then take the second-stage action from a feasible set that depends both on the first-stage decision and the model parameter. We aim to minimize the cumulative objective value while guaranteeing that the long-term average second-stage decision belongs to a set. We develop online algorithms for the online two-stage problem from adversarial learning algorithms. Also, the regret bound of our algorithm can be reduced to the regret bound of embedded adversarial learning algorithms. Based on this framework, we obtain new results under various settings. When the model parameters are drawn from unknown non-stationary distributions and we are given machine-learned predictions of the distributions, we develop a new algorithm from our framework with a regret $O(W_T+\sqrt{T})$, where $W_T$ measures the total inaccuracy of the machine-learned predictions. We then develop another algorithm that works when no machine-learned predictions are given and show the performances.

The goal of Continual Learning (CL) is to continuously learn from new data streams and accomplish the corresponding tasks. Previously studied CL assumes that data are given in sequence nose-to-tail for different tasks, thus indeed belonging to Serial Continual Learning (SCL). This paper studies the novel paradigm of Parallel Continual Learning (PCL) in dynamic multi-task scenarios, where a diverse set of tasks is encountered at different time points. PCL presents challenges due to the training of an unspecified number of tasks with varying learning progress, leading to the difficulty of guaranteeing effective model updates for all encountered tasks. In our previous conference work, we focused on measuring and reducing the discrepancy among gradients in a multi-objective optimization problem, which, however, may still contain negative transfers in every model update. To address this issue, in the dynamic multi-objective optimization problem, we introduce task-specific elastic factors to adjust the descent direction towards the Pareto front. The proposed method, called Elastic Multi-Gradient Descent (EMGD), ensures that each update follows an appropriate Pareto descent direction, minimizing any negative impact on previously learned tasks. To balance the training between old and new tasks, we also propose a memory editing mechanism guided by the gradient computed using EMGD. This editing process updates the stored data points, reducing interference in the Pareto descent direction from previous tasks. Experiments on public datasets validate the effectiveness of our EMGD in the PCL setting.

AI alignment aims to make AI systems behave in line with human intentions and values. As AI systems grow more capable, so do risks from misalignment. To provide a comprehensive and up-to-date overview of the alignment field, in this survey, we delve into the core concepts, methodology, and practice of alignment. First, we identify four principles as the key objectives of AI alignment: Robustness, Interpretability, Controllability, and Ethicality (RICE). Guided by these four principles, we outline the landscape of current alignment research and decompose them into two key components: forward alignment and backward alignment. The former aims to make AI systems aligned via alignment training, while the latter aims to gain evidence about the systems' alignment and govern them appropriately to avoid exacerbating misalignment risks. On forward alignment, we discuss techniques for learning from feedback and learning under distribution shift. On backward alignment, we discuss assurance techniques and governance practices. We also release and continually update the website (www.alignmentsurvey.com) which features tutorials, collections of papers, blog posts, and other resources.

In therapeutic design, balancing various physiochemical properties is crucial for molecule development, similar to how Multiparameter Optimization (MPO) evaluates multiple variables to meet a primary goal. While many molecular features can now be predicted using \textit{in silico} methods, aiding early drug development, the vast data generated from high throughput virtual screening challenges the practicality of traditional MPO approaches. Addressing this, we introduce a scaffold focused graph-based Markov chain Monte Carlo framework (ScaMARS) built to generate molecules with optimal properties. This innovative framework is capable of self-training and handling a wider array of properties, sampling different chemical spaces according to the starting scaffold. The benchmark analysis on several properties shows that ScaMARS has a diversity score of 84.6\% and has a much higher success rate of 99.5\% compared to conditional models. The integration of new features into MPO significantly enhances its adaptability and effectiveness in therapeutic design, facilitating the discovery of candidates that efficiently optimize multiple properties.

Curb space is one of the busiest areas in urban road networks. Especially in recent years, the rapid increase of ride-hailing trips and commercial deliveries has induced massive pick-ups/drop-offs (PUDOs), which occupy the limited curb space that was designed and built decades ago. These PUDOs could jam curbside utilization and disturb the mainline traffic flow, evidently leading to significant negative societal externalities. However, there is a lack of an analytical framework that rigorously quantifies and mitigates the congestion effect of PUDOs in the system view, particularly with little data support and involvement of confounding effects. To bridge this research gap, this paper develops a rigorous causal inference approach to estimate the congestion effect of PUDOs on general regional networks. A causal graph is set to represent the spatio-temporal relationship between PUDOs and traffic speed, and a double and separated machine learning (DSML) method is proposed to quantify how PUDOs affect traffic congestion. Additionally, a re-routing formulation is developed and solved to encourage passenger walking and traffic flow re-routing to achieve system optimization. Numerical experiments are conducted using real-world data in the Manhattan area. On average, 100 additional units of PUDOs in a region could reduce the traffic speed by 3.70 and 4.54 mph on weekdays and weekends, respectively. Re-routing trips with PUDOs on curb space could respectively reduce the system-wide total travel time by 2.44% and 2.12% in Midtown and Central Park on weekdays. Sensitivity analysis is also conducted to demonstrate the effectiveness and robustness of the proposed framework.

Nash equilibrium[1] of normal-form game was proposed decades ago, yet even whether PTAS exists for it remains undecided, not to mention for equilibriums of games with dynamics. PTAS for equilibriums of games is important itself in game theory, and the confirmation of its existence may impact multi-agent reinforcement learning research. First, the existence of PTAS relates to the practicality of the amount of computational power in achieving equilibriums of large scale games. It has been proved that exactly computing a Nash equilibrium of a static game is in PPAD-hard class of complexity[2]. Ignoring the possibility that PPAD itself is of polynomial-time[3], PTAS describes methods that approximately compute Nash equilibriums efficiently. Second, the confirmation of previously unknown existence of PTAS for games implies possibility to fundamentally solve the problems of non-stationarity in training and curse of dimensionality[4] in multi-agent reinforcement learning at the same time. Both the two problems are related to the absence of PTAS for equilibriums of games. Non-stationarity in training relates to the fact that existing polynomial-time methods lack convergence guarantee to equilibriums, and curse of dimensionality relates to the fact that methods with convergence guarantee lack polynomial-time complexity.

With the growth of 3D sensing technology, deep learning system for 3D point clouds has become increasingly important, especially in applications like autonomous vehicles where safety is a primary concern. However, there are also growing concerns about the reliability of these systems when they encounter noisy point clouds, whether occurring naturally or introduced with malicious intent. This paper highlights the challenges of point cloud classification posed by various forms of noise, from simple background noise to malicious backdoor attacks that can intentionally skew model predictions. While there's an urgent need for optimized point cloud denoising, current point outlier removal approaches, an essential step for denoising, rely heavily on handcrafted strategies and are not adapted for higher-level tasks, such as classification. To address this issue, we introduce an innovative point outlier cleansing method that harnesses the power of downstream classification models. By employing gradient-based attribution analysis, we define a novel concept: point risk. Drawing inspiration from tail risk minimization in finance, we recast the outlier removal process as an optimization problem, named PointCVaR. Extensive experiments show that our proposed technique not only robustly filters diverse point cloud outliers but also consistently and significantly enhances existing robust methods for point cloud classification.

Sliced Wasserstein (SW) distance suffers from redundant projections due to independent uniform random projecting directions. To partially overcome the issue, max K sliced Wasserstein (Max-K-SW) distance ($K\geq 1$), seeks the best discriminative orthogonal projecting directions. Despite being able to reduce the number of projections, the metricity of Max-K-SW cannot be guaranteed in practice due to the non-optimality of the optimization. Moreover, the orthogonality constraint is also computationally expensive and might not be effective. To address the problem, we introduce a new family of SW distances, named Markovian sliced Wasserstein (MSW) distance, which imposes a first-order Markov structure on projecting directions. We discuss various members of MSW by specifying the Markov structure including the prior distribution, the transition distribution, and the burning and thinning technique. Moreover, we investigate the theoretical properties of MSW including topological properties (metricity, weak convergence, and connection to other distances), statistical properties (sample complexity, and Monte Carlo estimation error), and computational properties (computational complexity and memory complexity). Finally, we compare MSW distances with previous SW variants in various applications such as gradient flows, color transfer, and deep generative modeling to demonstrate the favorable performance of MSW.

We study the sample complexity of sample average approximation (SAA) and its simple variations, referred to as the regularized SAA (RSAA), in solving convex and strongly convex stochastic programming (SP) problems under heavy-tailed-ness, non-Lipschitz-ness, and/or high dimensionality. The presence of such irregularities underscores critical vacua in the literature. In response, this paper presents three sets of results: First, we show that the (R)SAA is effective even if the objective function is not necessarily Lipschitz and the underlying distribution admits some bounded central moments only at (near-)optimal solutions. Second, when the SP's objective function is the sum of a smooth term and a Lipschitz term, we prove that the (R)SAA's sample complexity is completely independent from any complexity measures (e.g., the covering number) of the feasible region. Third, we explicate the (R)SAA's sample complexities with regard to the dependence on dimensionality $d$: When some $p$th ($p\geq 2$) central moment of the underlying distribution is bounded, we show that the required sample size grows at a rate no worse than $\mathcal O\left(p d^{2/p}\right)$ under any one of the three structural assumptions: (i) strong convexity w.r.t. the $q$-norm ($q\geq 1$); (ii) the combination of restricted strong convexity and sparsity; and (iii) a dimension-insensitive $q$-norm of an optimal solution. In both cases of (i) and (iii), it is further required that $p\leq q/(q-1)$. As a direct implication, the (R)SAA's complexity becomes (poly-)logarithmic in $d$, whenever $p\geq c\cdot \ln d$ is admissible for some constant $c>0$. These new results deviate from the SAA's typical sample complexities that grow polynomially with $d$. Part of our proof is based on the average-replace-one (RO) stability, which appears to be novel for the (R)SAA's analyses.