In numerous reinforcement learning (RL) problems involving safety-critical systems, a key challenge lies in balancing multiple objectives while simultaneously meeting all stringent safety constraints. To tackle this issue, we propose a primal-based framework that orchestrates policy optimization between multi-objective learning and constraint adherence. Our method employs a novel natural policy gradient manipulation method to optimize multiple RL objectives and overcome conflicting gradients between different tasks, since the simple weighted average gradient direction may not be beneficial for specific tasks' performance due to misaligned gradients of different task objectives. When there is a violation of a hard constraint, our algorithm steps in to rectify the policy to minimize this violation. We establish theoretical convergence and constraint violation guarantees in a tabular setting. Empirically, our proposed method also outperforms prior state-of-the-art methods on challenging safe multi-objective reinforcement learning tasks.

Lane detection is a fundamental task in autonomous driving. While the problem is typically formulated as the detection of continuous boundaries, we study the problem of detecting lane boundaries that are sparsely marked by 2D points with many false positives. This problem arises in the Formula Student Driverless (FSD) competition and is challenging due to its inherent ambiguity. Previous methods are inefficient and unable to find long-horizon solutions. We propose a deterministic algorithm called CLC that uses backtracking graph search with a learned likelihood function to overcome these limitations. We impose geometric constraints on the lane candidates to guarantee a geometrically sound lane. Our exhaustive search leads to finding the global optimum in 45% of instances, and the algorithm is overall robust to up to 50% false positives. Our algorithm runs in less than 15 ms on a single CPU core, meeting the low latency requirements of autonomous racing. We extensively evaluate our method on real data and realistic racetrack layouts, and show that it outperforms the state-of-the-art by detecting long lanes over 100 m with few (0.6%) critical failures. This allows our autonomous racecar to drive close to its physical limits on a previously unknown racetrack without being limited by perception. We release our dataset with realistic Formula Student racetracks to enable further research.

In constrained Markov decision processes (CMDPs) with adversarial rewards and constraints, a well-known impossibility result prevents any algorithm from attaining both sublinear regret and sublinear constraint violation, when competing against a best-in-hindsight policy that satisfies constraints on average. In this paper, we show that this negative result can be eased in CMDPs with non-stationary rewards and constraints, by providing algorithms whose performances smoothly degrade as non-stationarity increases. Specifically, we propose algorithms attaining $\tilde{\mathcal{O}} (\sqrt{T} + C)$ regret and positive constraint violation under bandit feedback, where $C$ is a corruption value measuring the environment non-stationarity. This can be $\Theta(T)$ in the worst case, coherently with the impossibility result for adversarial CMDPs. First, we design an algorithm with the desired guarantees when $C$ is known. Then, in the case $C$ is unknown, we show how to obtain the same results by embedding such an algorithm in a general meta-procedure. This is of independent interest, as it can be applied to any non-stationary constrained online learning setting.

This paper studies the challenge of developing robots capable of understanding under-specified instructions for creating functional object arrangements, such as "set up a dining table for two"; previous arrangement approaches have focused on much more explicit instructions, such as "put object A on the table." We introduce a framework, SetItUp, for learning to interpret under-specified instructions. SetItUp takes a small number of training examples and a human-crafted program sketch to uncover arrangement rules for specific scene types. By leveraging an intermediate graph-like representation of abstract spatial relationships among objects, SetItUp decomposes the arrangement problem into two subproblems: i) learning the arrangement patterns from limited data and ii) grounding these abstract relationships into object poses. SetItUp leverages large language models (LLMs) to propose the abstract spatial relationships among objects in novel scenes as the constraints to be satisfied; then, it composes a library of diffusion models associated with these abstract relationships to find object poses that satisfy the constraints. We validate our framework on a dataset comprising study desks, dining tables, and coffee tables, with the results showing superior performance in generating physically plausible, functional, and aesthetically pleasing object arrangements compared to existing models.

Reinforcement Learning (RL) for control has become increasingly popular due to its ability to learn rich feedback policies that take into account uncertainty and complex representations of the environment. When considering safety constraints, constrained optimization approaches, where agents are penalized for constraint violations, are commonly used. In such methods, if agents are initialized in, or must visit, states where constraint violation might be inevitable, it is unclear how much they should be penalized. We address this challenge by formulating a constraint on the counterfactual harm of the learned policy compared to a default, safe policy. In a philosophical sense this formulation only penalizes the learner for constraint violations that it caused; in a practical sense it maintains feasibility of the optimal control problem. We present simulation studies on a rover with uncertain road friction and a tractor-trailer parking environment that demonstrate our constraint formulation enables agents to learn safer policies than contemporary constrained RL methods.

When solving decision and optimisation problems, many competing algorithms (model and solver choices) have complementary strengths. Typically, there is no single algorithm that works well for all instances of a problem. Automated algorithm selection has been shown to work very well for choosing a suitable algorithm for a given instance. However, the cost of training can be prohibitively large due to running candidate algorithms on a representative set of training instances. In this work, we explore reducing this cost by choosing a subset of the training instances on which to train. We approach this problem in three ways: using active learning to decide based on prediction uncertainty, augmenting the algorithm predictors with a timeout predictor, and collecting training data using a progressively increasing timeout. We evaluate combinations of these approaches on six datasets from ASLib and present the reduction in labelling cost achieved by each option.

Two fundamental challenges face generative models in engineering applications: the acquisition of high-performing, diverse datasets, and the adherence to precise constraints in generated designs. We propose a novel approach combining optimization, constraint satisfaction, and language models to tackle these challenges in architectural design. Our method uses Quality-Diversity (QD) to generate a diverse, high-performing dataset. We then fine-tune a language model with this dataset to generate high-level designs. These designs are then refined into detailed, constraint-compliant layouts using the Wave Function Collapse algorithm. Our system demonstrates reliable adherence to textual guidance, enabling the generation of layouts with targeted architectural and performance features. Crucially, our results indicate that data synthesized through the evolutionary search of QD not only improves overall model performance but is essential for the model's ability to closely adhere to textual guidance. This improvement underscores the pivotal role evolutionary computation can play in creating the datasets key to training generative models for design. Web article at https://tilegpt.github.io

We consider the problem of constrained Markov decision process (CMDP) in continuous state-actions spaces where the goal is to maximize the expected cumulative reward subject to some constraints. We propose a novel Conservative Natural Policy Gradient Primal-Dual Algorithm (C-NPG-PD) to achieve zero constraint violation while achieving state of the art convergence results for the objective value function. For general policy parametrization, we prove convergence of value function to global optimal upto an approximation error due to restricted policy class. We even improve the sample complexity of existing constrained NPG-PD algorithm \cite{Ding2020} from $\mathcal{O}(1/\epsilon^6)$ to $\mathcal{O}(1/\epsilon^4)$. To the best of our knowledge, this is the first work to establish zero constraint violation with Natural policy gradient style algorithms for infinite horizon discounted CMDPs. We demonstrate the merits of proposed algorithm via experimental evaluations.

A well-studied generalization of the standard online convex optimization (OCO) is constrained online convex optimization (COCO). In COCO, on every round, a convex cost function and a convex constraint function are revealed to the learner after the action for that round is chosen. The objective is to design an online policy that simultaneously achieves a small regret while ensuring small cumulative constraint violation (CCV) against an adaptive adversary. A long-standing open question in COCO is whether an online policy can simultaneously achieve $O(\sqrt{T})$ regret and $O(\sqrt{T})$ CCV without any restrictive assumptions. For the first time, we answer this in the affirmative and show that an online policy can simultaneously achieve $O(\sqrt{T})$ regret and $\tilde{O}(\sqrt{T})$ CCV. We establish this result by effectively combining the adaptive regret bound of the AdaGrad algorithm with Lyapunov optimization - a classic tool from control theory. Surprisingly, the analysis is short and elegant.

The uses of machine learning (ML) have snowballed in recent years. In many cases, ML models are highly complex, and their operation is beyond the understanding of human decision-makers. Nevertheless, some uses of ML models involve high-stakes and safety-critical applications. Explainable artificial intelligence (XAI) aims to help human decision-makers in understanding the operation of such complex ML models, thus eliciting trust in their operation. Unfortunately, the majority of past XAI work is based on informal approaches, that offer no guarantees of rigor. Unsurprisingly, there exists comprehensive experimental and theoretical evidence confirming that informal methods of XAI can provide human-decision makers with erroneous information. Logic-based XAI represents a rigorous approach to explainability; it is model-based and offers the strongest guarantees of rigor of computed explanations. However, a well-known drawback of logic-based XAI is the complexity of logic reasoning, especially for highly complex ML models. Recent work proposed distance-restricted explanations, i.e. explanations that are rigorous provided the distance to a given input is small enough. Distance-restricted explainability is tightly related with adversarial robustness, and it has been shown to scale for moderately complex ML models, but the number of inputs still represents a key limiting factor. This paper investigates novel algorithms for scaling up the performance of logic-based explainers when computing and enumerating ML model explanations with a large number of inputs.