Loco-manipulation planning skills are pivotal for expanding the utility of robots in everyday environments. These skills can be assessed based on a system's ability to coordinate complex holistic movements and multiple contact interactions when solving different tasks. However, existing approaches have been merely able to shape such behaviors with hand-crafted state machines, densely engineered rewards, or pre-recorded expert demonstrations. Here, we propose a minimally-guided framework that automatically discovers whole-body trajectories jointly with contact schedules for solving general loco-manipulation tasks in pre-modeled environments. The key insight is that multi-modal problems of this nature can be formulated and treated within the context of integrated Task and Motion Planning (TAMP). An effective bilevel search strategy is achieved by incorporating domain-specific rules and adequately combining the strengths of different planning techniques: trajectory optimization and informed graph search coupled with sampling-based planning. We showcase emergent behaviors for a quadrupedal mobile manipulator exploiting both prehensile and non-prehensile interactions to perform real-world tasks such as opening/closing heavy dishwashers and traversing spring-loaded doors. These behaviors are also deployed on the real system using a two-layer whole-body tracking controller.

Pearl's do calculus is a complete axiomatic approach to learn the identifiable causal effects from observational data. When such an effect is not identifiable, it is necessary to perform a collection of often costly interventions in the system to learn the causal effect. In this work, we consider the problem of designing the collection of interventions with the minimum cost to identify the desired effect. First, we prove that this problem is NP-hard, and subsequently propose an algorithm that can either find the optimal solution or a logarithmic-factor approximation of it. This is done by establishing a connection between our problem and the minimum hitting set problem. Additionally, we propose several polynomial-time heuristic algorithms to tackle the computational complexity of the problem. Although these algorithms could potentially stumble on sub-optimal solutions, our simulations show that they achieve small regrets on random graphs.

Restless multi-armed bandits (RMABs) are a popular framework for algorithmic decision making in sequential settings with limited resources. RMABs are increasingly being used for sensitive decisions such as in public health, treatment scheduling, anti-poaching, and -- the motivation for this work -- digital health. For such high stakes settings, decisions must both improve outcomes and prevent disparities between groups (e.g., ensure health equity). We study equitable objectives for RMABs (ERMABs) for the first time. We consider two equity-aligned objectives from the fairness literature, minimax reward and max Nash welfare. We develop efficient algorithms for solving each -- a water filling algorithm for the former, and a greedy algorithm with theoretically motivated nuance to balance disparate group sizes for the latter. Finally, we demonstrate across three simulation domains, including a new digital health model, that our approaches can be multiple times more equitable than the current state of the art without drastic sacrifices to utility. Our findings underscore our work's urgency as RMABs permeate into systems that impact human and wildlife outcomes. Code is available at https://github.com/google-research/socialgood/tree/equitable-rmab

Researchers constantly strive to explore larger and more complex search spaces in various scientific studies and physical experiments. However, such investigations often involve sophisticated simulators or time-consuming experiments that make exploring and observing new design samples challenging. Previous works that target such applications are typically sample-inefficient and restricted to vector search spaces. To address these limitations, this work proposes a constrained multi-objective optimization (MOO) framework, called BREATHE, that searches not only traditional vector-based design spaces but also graph-based design spaces to obtain best-performing graphs. It leverages second-order gradients and actively trains a heteroscedastic surrogate model for sample-efficient optimization. In a single-objective vector optimization application, it leads to 64.1% higher performance than the next-best baseline, random forest regression. In graph-based search, BREATHE outperforms the next-best baseline, i.e., a graphical version of Gaussian-process-based Bayesian optimization, with up to 64.9% higher performance. In a MOO task, it achieves up to 21.9$\times$ higher hypervolume than the state-of-the-art method, multi-objective Bayesian optimization (MOBOpt). BREATHE also outperforms the baseline methods on most standard MOO benchmark applications.

Federated Learning (FL) is a distributed machine learning (ML) paradigm, in which multiple clients collaboratively train ML models without centralizing their local data. Similar to conventional ML pipelines, the client local optimization and server aggregation procedure in FL are sensitive to the hyperparameter (HP) selection. Despite extensive research on tuning HPs for centralized ML, these methods yield suboptimal results when employed in FL. This is mainly because their "training-after-tuning" framework is unsuitable for FL with limited client computation power. While some approaches have been proposed for HP-Tuning in FL, they are limited to the HPs for client local updates. In this work, we propose a novel HP-tuning algorithm, called Federated Population-based Hyperparameter Tuning (FedPop), to address this vital yet challenging problem. FedPop employs population-based evolutionary algorithms to optimize the HPs, which accommodates various HP types at both client and server sides. Compared with prior tuning methods, FedPop employs an online "tuning-while-training" framework, offering computational efficiency and enabling the exploration of a broader HP search space. Our empirical validation on the common FL benchmarks and complex real-world FL datasets demonstrates the effectiveness of the proposed method, which substantially outperforms the concurrent state-of-the-art HP tuning methods for FL.

Symmetry and dominance breaking can be crucial for solving hard combinatorial search and optimisation problems, but the correctness of these techniques sometimes relies on subtle arguments. For this reason, it is desirable to produce efficient, machine-verifiable certificates that solutions have been computed correctly. Building on the cutting planes proof system, we develop a certification method for optimisation problems in which symmetry and dominance breaking is easily expressible. Our experimental evaluation demonstrates that we can efficiently verify fully general symmetry breaking in Boolean satisfiability (SAT) solving, thus providing, for the first time, a unified method to certify a range of advanced SAT techniques that also includes cardinality and parity (XOR) reasoning. In addition, we apply our method to maximum clique solving and constraint programming as a proof of concept that the approach applies to a wider range of combinatorial problems.

This paper introduces a novel algorithm for solving the point-to-point shortest path problem in a static regular 8-neighbor connectivity (G8) grid. This algorithm can be seen as a generalization of Hadlock algorithm to G8 grids, and is shown to be theoretically equivalent to the relaxed $A^*$ ($RA^*$) algorithm in terms of the provided solution's path length, but with substantial time and memory savings, due to a completely different computation strategy, based on defining a set of lookup matrices. Through an experimental study on grid maps of various types and sizes (1290 runs on 43 maps), it is proven to be 2.25 times faster than $RA^*$ and 17 times faster than the original $A^*$, in average. Moreover, it is more memory-efficient, since it does not need to store a G score matrix.

The shortest path problem in graphs is fundamental to AI. Nearly all variants of the problem and relevant algorithms that solve them ignore edge-weight computation time and its common relation to weight uncertainty. This implies that taking these factors into consideration can potentially lead to a performance boost in relevant applications. Recently, a generalized framework for weighted directed graphs was suggested, where edge-weight can be computed (estimated) multiple times, at increasing accuracy and run-time expense. We build on this framework to introduce the problem of finding the tightest admissible shortest path (TASP); a path with the tightest suboptimality bound on the optimal cost. This is a generalization of the shortest path problem to bounded uncertainty, where edge-weight uncertainty can be traded for computational cost. We present a complete algorithm for solving TASP, with guarantees on solution quality. Empirical evaluation supports the effectiveness of this approach.

We study how to efficiently combine formal methods, Monte Carlo Tree Search (MCTS), and deep learning in order to produce high-quality receding horizon policies in large Markov Decision processes (MDPs). In particular, we use model-checking techniques to guide the MCTS algorithm in order to generate offline samples of high-quality decisions on a representative set of states of the MDP. Those samples can then be used to train a neural network that imitates the policy used to generate them. This neural network can either be used as a guide on a lower-latency MCTS online search, or alternatively be used as a full-fledged policy when minimal latency is required. We use statistical model checking to detect when additional samples are needed and to focus those additional samples on configurations where the learnt neural network policy differs from the (computationally-expensive) offline policy. We illustrate the use of our method on MDPs that model the Frozen Lake and Pac-Man environments -- two popular benchmarks to evaluate reinforcement-learning algorithms.

Piecewise-affine (PWA) systems are widely used for modeling and control of robotics problems including modeling contact dynamics. A common approach is to encode the control problem of the PWA system as a Mixed-Integer Convex Program (MICP), which can be solved by general-purpose off-the-shelf MICP solvers. To mitigate the scalability challenge of solving these MICP problems, existing work focuses on devising efficient and strong formulations of the problems, while less effort has been spent on exploiting their specific structure to develop specialized solvers. The latter is the theme of our work. We focus on efficiently handling one-hot constraints, which are particularly relevant when encoding PWA dynamics. We have implemented our techniques in a tool, Soy, which organically integrates logical reasoning, arithmetic reasoning, and stochastic local search. For a set of PWA control benchmarks, Soy solves more problems, faster, than two state-of-the-art MICP solvers.