Reliable and efficient trajectory optimization methods are a fundamental need for autonomous dynamical systems, effectively enabling applications including rocket landing, hypersonic reentry, spacecraft rendezvous, and docking. Within such safety-critical application areas, the complexity of the emerging trajectory optimization problems has motivated the application of AI-based techniques to enhance the performance of traditional approaches. However, current AI-based methods either attempt to fully replace traditional control algorithms, thus lacking constraint satisfaction guarantees and incurring in expensive simulation, or aim to solely imitate the behavior of traditional methods via supervised learning. To address these limitations, this paper proposes the Autonomous Rendezvous Transformer (ART) and assesses the capability of modern generative models to solve complex trajectory optimization problems, both from a forecasting and control standpoint. Specifically, this work assesses the capabilities of Transformers to (i) learn near-optimal policies from previously collected data, and (ii) warm-start a sequential optimizer for the solution of non-convex optimal control problems, thus guaranteeing hard constraint satisfaction. From a forecasting perspective, results highlight how ART outperforms other learning-based architectures at predicting known fuel-optimal trajectories. From a control perspective, empirical analyses show how policies learned through Transformers are able to generate near-optimal warm-starts, achieving trajectories that are (i) more fuel-efficient, (ii) obtained in fewer sequential optimizer iterations, and (iii) computed with an overall runtime comparable to benchmarks based on convex optimization.
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Causal effect estimation from observational data is a fundamental task in empirical sciences. It becomes particularly challenging when unobserved confounders are involved in a system. This paper focuses on front-door adjustment -- a classic technique which, using observed mediators allows to identify causal effects even in the presence of unobserved confounding. While the statistical properties of the front-door estimation are quite well understood, its algorithmic aspects remained unexplored for a long time. In 2022, Jeong, Tian, and Bareinboim presented the first polynomial-time algorithm for finding sets satisfying the front-door criterion in a given directed acyclic graph (DAG), with an $O(n^3(n+m))$ run time, where $n$ denotes the number of variables and $m$ the number of edges of the causal graph. In our work, we give the first linear-time, i.e., $O(n+m)$, algorithm for this task, which thus reaches the asymptotically optimal time complexity. This result implies an $O(n(n+m))$ delay enumeration algorithm of all front-door adjustment sets, again improving previous work by a factor of $n^3$. Moreover, we provide the first linear-time algorithm for finding a minimal front-door adjustment set. We offer implementations of our algorithms in multiple programming languages to facilitate practical usage and empirically validate their feasibility, even for large graphs.
In the feature space, the collapse between features invokes critical problems in representation learning by remaining the features undistinguished. Interpolation-based augmentation methods such as mixup have shown their effectiveness in relieving the collapse problem between different classes, called inter-class collapse. However, intra-class collapse raised in coarse-to-fine transfer learning has not been discussed in the augmentation approach. To address them, we propose a better feature augmentation method, asymptotic midpoint mixup. The method generates augmented features by interpolation but gradually moves them toward the midpoint of inter-class feature pairs. As a result, the method induces two effects: 1) balancing the margin for all classes and 2) only moderately broadening the margin until it holds maximal confidence. We empirically analyze the collapse effects by measuring alignment and uniformity with visualizing representations. Then, we validate the intra-class collapse effects in coarse-to-fine transfer learning and the inter-class collapse effects in imbalanced learning on long-tailed datasets. In both tasks, our method shows better performance than other augmentation methods.
Randomized controlled trials (RCTs) serve as the cornerstone for understanding causal effects, yet extending inferences to target populations presents challenges due to effect heterogeneity and underrepresentation. Our paper addresses the critical issue of identifying and characterizing underrepresented subgroups in RCTs, proposing a novel framework for refining target populations to improve generalizability. We introduce an optimization-based approach, Rashomon Set of Optimal Trees (ROOT), to characterize underrepresented groups. ROOT optimizes the target subpopulation distribution by minimizing the variance of the target average treatment effect estimate, ensuring more precise treatment effect estimations. Notably, ROOT generates interpretable characteristics of the underrepresented population, aiding researchers in effective communication. Our approach demonstrates improved precision and interpretability compared to alternatives, as illustrated with synthetic data experiments. We apply our methodology to extend inferences from the Starting Treatment with Agonist Replacement Therapies (START) trial -- investigating the effectiveness of medication for opioid use disorder -- to the real-world population represented by the Treatment Episode Dataset: Admissions (TEDS-A). By refining target populations using ROOT, our framework offers a systematic approach to enhance decision-making accuracy and inform future trials in diverse populations.
We present an experimental validation of a recently proposed optimization technique for reservoir computing, using an optoelectronic setup. Reservoir computing is a robust framework for signal processing applications, and the development of efficient optimization approaches remains a key challenge. The technique we address leverages solely a delayed version of the input signal to identify the optimal operational region of the reservoir, simplifying the traditionally time-consuming task of hyperparameter tuning. We verify the effectiveness of this approach on different benchmark tasks and reservoir operating conditions.
Correlation clustering is a well-known unsupervised learning setting that deals with positive and negative pairwise similarities. In this paper, we study the case where the pairwise similarities are not given in advance and must be queried in a cost-efficient way. Thereby, we develop a generic active learning framework for this task that benefits from several advantages, e.g., flexibility in the type of feedback that a user/annotator can provide, adaptation to any correlation clustering algorithm and query strategy, and robustness to noise. In addition, we propose and analyze a number of novel query strategies suited to this setting. We demonstrate the effectiveness of our framework and the proposed query strategies via several experimental studies.
Many stochastic continuous-state dynamical systems can be modeled as probabilistic programs with nonlinear non-polynomial updates in non-nested loops. We present two methods, one approximate and one exact, to automatically compute, without sampling, moment-based invariants for such probabilistic programs as closed-form solutions parameterized by the loop iteration. The exact method applies to probabilistic programs with trigonometric and exponential updates and is embedded in the Polar tool. The approximate method for moment computation applies to any nonlinear random function as it exploits the theory of polynomial chaos expansion to approximate non-polynomial updates as the sum of orthogonal polynomials. This translates the dynamical system to a non-nested loop with polynomial updates, and thus renders it conformable with the Polar tool that computes the moments of any order of the state variables. We evaluate our methods on an extensive number of examples ranging from modeling monetary policy to several physical motion systems in uncertain environments. The experimental results demonstrate the advantages of our approach with respect to the current state-of-the-art.
Counterfactuals and counterfactual reasoning underpin numerous techniques for auditing and understanding artificial intelligence (AI) systems. The traditional paradigm for counterfactual reasoning in this literature is the interventional counterfactual, where hypothetical interventions are imagined and simulated. For this reason, the starting point for causal reasoning about legal protections and demographic data in AI is an imagined intervention on a legally-protected characteristic, such as ethnicity, race, gender, disability, age, etc. We ask, for example, what would have happened had your race been different? An inherent limitation of this paradigm is that some demographic interventions -- like interventions on race -- may not translate into the formalisms of interventional counterfactuals. In this work, we explore a new paradigm based instead on the backtracking counterfactual, where rather than imagine hypothetical interventions on legally-protected characteristics, we imagine alternate initial conditions while holding these characteristics fixed. We ask instead, what would explain a counterfactual outcome for you as you actually are or could be? This alternate framework allows us to address many of the same social concerns, but to do so while asking fundamentally different questions that do not rely on demographic interventions.
Influential diagnosis is an integral part of data analysis, of which most existing methodological frameworks presume a deterministic submodel and are designed for low-dimensional data (i.e., the number of predictors p smaller than the sample size n). However, the stochastic selection of a submodel from high-dimensional data where p exceeds n has become ubiquitous. Thus, methods for identifying observations that could exert undue influence on the choice of a submodel can play an important role in this setting. To date, discussion of this topic has been limited, falling short in two domains: (i) constrained ability to detect multiple influential points, and (ii) applicability only in restrictive settings. After describing the problem, we characterize and formalize the concept of influential observations on variable selection. Then, we propose a generalized diagnostic measure, extended from an available metric accommodating different model selectors and multiple influential observations, the asymptotic distribution of which is subsequently establish large p, thus providing guidelines to ascertain influential observations. A high-dimensional clustering procedure is further incorporated into our proposed scheme to detect multiple influential points. Simulation is conducted to assess the performances of various diagnostic approaches. The proposed procedure further demonstrates its value in improving predictive power when analyzing thermal-stimulated pain based on fMRI data.
In practical communication systems, knowledge of channel models is often absent, and consequently, transceivers need be designed based on empirical data. In this work, we study data-driven approaches to reliably choosing decoding metrics and code rates that facilitate reliable communication over unknown discrete memoryless channels (DMCs). Our analysis is inspired by the PAC learning theory and does not rely on any assumptions on the statistical characteristics of DMCs. We show that a naive plug-in algorithm for choosing decoding metrics is likely to fail for finite training sets. We propose an alternative algorithm called the virtual sample algorithm and establish a non-asymptotic lower bound on its performance. The virtual sample algorithm is then used as a building block for constructing a learning algorithm that chooses a decoding metric and a code rate using which a transmitter and a receiver can reliably communicate at a rate arbitrarily close to the channel mutual information. Therefore, we conclude that DMCs are PAC learnable.
Detecting carried objects is one of the requirements for developing systems to reason about activities involving people and objects. We present an approach to detect carried objects from a single video frame with a novel method that incorporates features from multiple scales. Initially, a foreground mask in a video frame is segmented into multi-scale superpixels. Then the human-like regions in the segmented area are identified by matching a set of extracted features from superpixels against learned features in a codebook. A carried object probability map is generated using the complement of the matching probabilities of superpixels to human-like regions and background information. A group of superpixels with high carried object probability and strong edge support is then merged to obtain the shape of the carried object. We applied our method to two challenging datasets, and results show that our method is competitive with or better than the state-of-the-art.
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