Line search procedures are often employed in primal-dual methods for bilinear saddle point problems, especially when the norm of the linear operator is large or difficult to compute. In this paper, we demonstrate that line search is unnecessary by introducing a novel primal-dual method, the auto-conditioned primal-dual hybrid gradient (AC-PDHG) method, which achieves optimal complexity for solving bilinear saddle point problems. AC-PDHG is fully adaptive to the linear operator, using only past iterates to estimate its norm. We further tailor AC-PDHG to solve linearly constrained problems, providing convergence guarantees for both the optimality gap and constraint violation. Moreover, we explore an important class of linearly constrained problems where both the objective and constraints decompose into two parts. By incorporating the design principles of AC-PDHG into the preconditioned alternating direction method of multipliers (ADMM), we propose the auto-conditioned alternating direction method of multipliers (AC-ADMM), which guarantees convergence based solely on one part of the constraint matrix and fully adapts to it, eliminating the need for line search. Finally, we extend both AC-PDHG and AC-ADMM to solve bilinear problems with an additional smooth term. By integrating these methods with a novel acceleration scheme, we attain optimal iteration complexities under the single-oracle setting.

Enforcing state-wise safety constraints is critical for the application of reinforcement learning (RL) in real-world problems, such as autonomous driving and robot manipulation. However, existing safe RL methods only enforce state-wise constraints in expectation or enforce hard state-wise constraints with strong assumptions. The former does not exclude the probability of safety violations, while the latter is impractical. Our insight is that although it is intractable to guarantee hard state-wise constraints in a model-free setting, we can enforce state-wise safety with high probability while excluding strong assumptions. To accomplish the goal, we propose Absolute State-wise Constrained Policy Optimization (ASCPO), a novel general-purpose policy search algorithm that guarantees high-probability state-wise constraint satisfaction for stochastic systems. We demonstrate the effectiveness of our approach by training neural network policies for extensive robot locomotion tasks, where the agent must adhere to various state-wise safety constraints. Our results show that ASCPO significantly outperforms existing methods in handling state-wise constraints across challenging continuous control tasks, highlighting its potential for real-world applications.

--Model-based control faces fundamental challenges in partially-observable environments due to unmodeled obstacles. We propose an online learning and optimization method to identify and avoid unobserved obstacles online. Our method, Constraint Obeying Gaussian Implicit Surfaces (COGIS), infers contact data using a combination of visual input and state tracking, informed by predictions from a nominal dynamics model. We then fit a Gaussian process implicit surface (GPIS) to these data and refine the dataset through a novel method of enforcing constraints on the estimated surface. This allows us to design a Model Predictive Control (MPC) method that leverages the obstacle estimate to complete multiple manipulation tasks. By modeling the environment instead of attempting to directly adapt the dynamics, our method succeeds at both low-dimensional peg-in-hole tasks and high-dimensional deformable object manipulation tasks. Our method succeeds in 10/10 trials vs 1/10 for a baseline on a real-world cable manipulation task under partial observability of the environment. PECIAL care must be taken when using model-based planning and control methods in partially observable environments. This is particularly important where not all obstacles are modeled by dynamics, to avoid collisions with unmodeled or unobserved parts of the environment. Such collisions could prevent task completion; for instance, the object being manipulated might be blocked by the unmodeled environment object. The challenge is heightened when manipulating deformable objects like cables in the home or office. This creates more possibilities for task failure.

Goal instructions for autonomous AI agents cannot assume that objects have unique names. Instead, objects in goals must be referred to by providing suitable descriptions. However, this raises problems in both classical planning and generalized planning. The standard approach to handling existentially quantified goals in classical planning involves compiling them into a DNF formula that encodes all possible variable bindings and adding dummy actions to map each DNF term into the new, dummy goal. This preprocessing is exponential in the number of variables. In generalized planning, the problem is different: even if general policies can deal with any initial situation and goal, executing a general policy requires the goal to be grounded to define a value for the policy features. The problem of grounding goals, namely finding the objects to bind the goal variables, is subtle: it is a generalization of classical planning, which is a special case when there are no goal variables to bind, and constraint reasoning, which is a special case when there are no actions. In this work, we address the goal grounding problem with a novel supervised learning approach. A GNN architecture, trained to predict the cost of partially quantified goals over small domain instances is tested on larger instances involving more objects and different quantified goals. The proposed architecture is evaluated experimentally over several planning domains where generalization is tested along several dimensions including the number of goal variables and objects that can bind such variables. The scope of the approach is also discussed in light of the known relationship between GNNs and C2 logics.

Imitation learning (IL) has shown great success in learning complex robot manipulation tasks. However, there remains a need for practical safety methods to justify widespread deployment. In particular, it is important to certify that a system obeys hard constraints on unsafe behavior in settings when it is unacceptable to design a tradeoff between performance and safety via tuning the policy (i.e. soft constraints). This leads to the question, how does enforcing hard constraints impact the performance (meaning safely completing tasks) of an IL policy? To answer this question, this paper builds a reachability-based safety filter to enforce hard constraints on IL, which we call Reachability-Aided Imitation Learning (RAIL). Through evaluations with state-of-the-art IL policies in mobile robots and manipulation tasks, we make two key findings. First, the highest-performing policies are sometimes only so because they frequently violate constraints, and significantly lose performance under hard constraints. Second, surprisingly, hard constraints on the lower-performing policies can occasionally increase their ability to perform tasks safely. Finally, hardware evaluation confirms the method can operate in real time.

Allocation tasks represent a class of problems where a limited amount of resources must be allocated to a set of entities at each time step. Prominent examples of this task include portfolio optimization or distributing computational workloads across servers. Allocation tasks are typically bound by linear constraints describing practical requirements that have to be strictly fulfilled at all times. In portfolio optimization, for example, investors may be obligated to allocate less than 30\% of the funds into a certain industrial sector in any investment period. Such constraints restrict the action space of allowed allocations in intricate ways, which makes learning a policy that avoids constraint violations difficult. In this paper, we propose a new method for constrained allocation tasks based on an autoregressive process to sequentially sample allocations for each entity. In addition, we introduce a novel de-biasing mechanism to counter the initial bias caused by sequential sampling. We demonstrate the superior performance of our approach compared to a variety of Constrained Reinforcement Learning (CRL) methods on three distinct constrained allocation tasks: portfolio optimization, computational workload distribution, and a synthetic allocation benchmark. Our code is available at: https://github.com/niklasdbs/paspo

Learning to plan for multi-step, multi-manipulator tasks is notoriously difficult because of the large search space and the complex constraint satisfaction problems. We present Generative Factor Chaining~(GFC), a composable generative model for planning. GFC represents a planning problem as a spatial-temporal factor graph, where nodes represent objects and robots in the scene, spatial factors capture the distributions of valid relationships among nodes, and temporal factors represent the distributions of skill transitions. Each factor is implemented as a modular diffusion model, which are composed during inference to generate feasible long-horizon plans through bi-directional message passing. We show that GFC can solve complex bimanual manipulation tasks and exhibits strong generalization to unseen planning tasks with novel combinations of objects and constraints. More details can be found at: https://generative-fc.github.io/

We propose a graph SLAM algorithm for sparse range sensing that incorporates a soft Manhattan world utilizing landmark-landmark constraints. Sparse range sensing is necessary for tiny robots that do not have the luxury of using heavy and expensive sensors. Existing SLAM methods dealing with sparse range sensing lack accuracy and accumulate drift error over time due to limited access to data points. Algorithms that cover this flaw using structural regularities, such as the Manhattan world (MW), have shortcomings when mapping real-world environments that do not coincide with the rules. We propose SoMaSLAM, a 2D graph SLAM designed for tiny robots with sparse range sensing. Our approach effectively maps sparse range data without enforcing strict structural regularities and maintains an adaptive graph. We implement the MW assumption as soft constraints, which we refer to as a soft Manhattan world. We propose novel soft landmark-landmark constraints to incorporate the soft MW into graph SLAM. Through extensive evaluation, we demonstrate that our proposed SoMaSLAM method improves localization accuracy on diverse datasets and is flexible enough to be used in the real world. We release our source code and sparse range datasets at https://SoMaSLAM.github.io/.

Constraint modelling languages such as Essence offer a means to describe combinatorial problems at a high-level, i.e., without committing to detailed modelling decisions for a particular solver or solving paradigm. Given a problem description written in Essence, there are multiple ways to translate it to a low-level constraint model. Choosing the right combination of a low-level constraint model and a target constraint solver can have significant impact on the effectiveness of the solving process. Furthermore, the choice of the best combination of constraint model and solver can be instance-dependent, i.e., there may not exist a single combination that works best for all instances of the same problem. In this paper, we consider the task of building machine learning models to automatically select the best combination for a problem instance. A critical part of the learning process is to define instance features, which serve as input to the selection model. Our contribution is automatic learning of instance features directly from the high-level representation of a problem instance using a language model. We evaluate the performance of our approach using the Essence modelling language with a case study involving the car sequencing problem.

Generative AI agents are often expected to respond to complex user requests that have No One Right Answer (NORA), e.g., "design a vegetarian meal plan below 1800 calories". Such requests may entail a set of constraints that the agent should adhere to. To successfully develop agents for NORA scenarios, an accurate automatic evaluation framework is essential, and specifically - one capable of validating the satisfaction of constraints in the agent's response. Recently, large language models (LLMs) have been adopted as versatile evaluators for many NORA tasks, but their ability to evaluate constraint-satisfaction in generated text remains unclear. To study this, we develop and release a novel Arithmetic Constraint-Satisfaction (ACS) benchmarking dataset. The dataset consists of complex user requests with corresponding constraints, agent responses and human labels indicating each constraint's satisfaction level in the response. A unique property of this dataset is that validating many of its constraints requires reviewing the response as a whole (in contrast to many other benchmarks that require the validation of a single independent item). Moreover, it assesses LLMs in performing reasoning, in-context data extraction, arithmetic calculations, and counting. We then benchmark both open and proprietary LLMs on evaluating constraint-satisfaction, and show that most models still have a significant headroom for improvement, and that errors primarily stem from reasoning issues. In addition, most models exhibit a skewed constraint-satisfaction prediction pattern, with higher accuracy where the ground-truth label is "satisfied". Lastly, few-shot prompting for our task proved to be rather challenging, since many of the studied models showed a degradation in performance when it was introduced.