A tremendous range of design tasks in materials, physics, and biology can be formulated as finding the optimum of an objective function depending on many parameters without knowing its closed-form expression or the derivative. Traditional derivative-free optimization techniques often rely on strong assumptions about objective functions, thereby failing at optimizing non-convex systems beyond 100 dimensions. Here, we present a tree search method for derivative-free optimization that enables accelerated optimal design of high-dimensional complex systems. Specifically, we introduce stochastic tree expansion, dynamic upper confidence bound, and short-range backpropagation mechanism to evade local optimum, iteratively approximating the global optimum using machine learning models. This development effectively confronts the dimensionally challenging problems, achieving convergence to global optima across various benchmark functions up to 2,000 dimensions, surpassing the existing methods by 10- to 20-fold. Our method demonstrates wide applicability to a wide range of real-world complex systems spanning materials, physics, and biology, considerably outperforming state-of-the-art algorithms. This enables efficient autonomous knowledge discovery and facilitates self-driving virtual laboratories. Although we focus on problems within the realm of natural science, the advancements in optimization techniques achieved herein are applicable to a broader spectrum of challenges across all quantitative disciplines.

Dynamic movements are ubiquitous in human motor behavior as they tend to be more efficient and can solve a broader range of skill domains than their quasi-static counterparts. For decades, robotic juggling tasks have been among the most frequently studied dynamic manipulation problems since the required dynamic dexterity can be scaled to arbitrarily high difficulty. However, successful approaches have been limited to basic juggling skills, indicating a lack of understanding of the required constraints for dexterous toss juggling. We present a detailed analysis of the toss juggling task, identifying the key challenges and formalizing it as a trajectory optimization problem. Building on our state-of-the-art, real-world toss juggling platform, we reach the theoretical limits of toss juggling in simulation, evaluate a resulting real-time controller in environments of varying difficulty and achieve robust toss juggling of up to 17 balls on two anthropomorphic manipulators.

Tendon-driven continuum robot kinematic models are frequently computationally expensive, inaccurate due to unmodeled effects, or both. In particular, unmodeled effects produce uncertainties that arise during the robot's operation that lead to variability in the resulting geometry. We propose a novel solution to these issues through the development of a Gaussian mixture kinematic model. We train a mixture density network to output a Gaussian mixture model representation of the robot geometry given the current tendon displacements. This model computes a probability distribution that is more representative of the true distribution of geometries at a given configuration than a model that outputs a single geometry, while also reducing the computation time. We demonstrate one use of this model through a trajectory optimization method that explicitly reasons about the workspace uncertainty to minimize the probability of collision.

Enabling robots to understand the world in terms of objects is a critical building block towards higher level autonomy. The success of foundation models in vision has created the ability to segment and identify nearly all objects in the world. However, utilizing such objects to localize the robot and build an open-set semantic map of the world remains an open research question. In this work, a system of identifying, localizing, and encoding objects is tightly coupled with probabilistic graphical models for performing open-set semantic simultaneous localization and mapping (SLAM). Results are presented demonstrating that the proposed lightweight object encoding can be used to perform more accurate object-based SLAM than existing open-set methods, closed-set methods, and geometric methods while incurring a lower computational overhead than existing open-set mapping methods.

This paper proposes a practically efficient algorithm with optimal theoretical regret which solves the classical network revenue management (NRM) problem with unknown, nonparametric demand. Over a time horizon of length $T$, in each time period the retailer needs to decide prices of $N$ types of products which are produced based on $M$ types of resources with unreplenishable initial inventory. When demand is nonparametric with some mild assumptions, Miao and Wang (2021) is the first paper which proposes an algorithm with $O(\text{poly}(N,M,\ln(T))\sqrt{T})$ type of regret (in particular, $\tilde O(N^{3.5}\sqrt{T})$ plus additional high-order terms that are $o(\sqrt{T})$ with sufficiently large $T\gg N$). In this paper, we improve the previous result by proposing a primal-dual optimization algorithm which is not only more practical, but also with an improved regret of $\tilde O(N^{3.25}\sqrt{T})$ free from additional high-order terms. A key technical contribution of the proposed algorithm is the so-called demand balancing, which pairs the primal solution (i.e., the price) in each time period with another price to offset the violation of complementary slackness on resource inventory constraints. Numerical experiments compared with several benchmark algorithms further illustrate the effectiveness of our algorithm.

Adam with decoupled weight decay, also known as AdamW, is widely acclaimed for its superior performance in language modeling tasks, surpassing Adam with $\ell_2$ regularization in terms of generalization and optimization. However, this advantage is not theoretically well-understood. One challenge here is that though intuitively Adam with $\ell_2$ regularization optimizes the $\ell_2$ regularized loss, it is not clear if AdamW optimizes a specific objective. In this work, we make progress toward understanding the benefit of AdamW by showing that it implicitly performs constrained optimization. More concretely, we show in the full-batch setting, if AdamW converges with any non-increasing learning rate schedule whose partial sum diverges, it must converge to a KKT point of the original loss under the constraint that the $\ell_\infty$ norm of the parameter is bounded by the inverse of the weight decay factor. This result is built on the observation that Adam can be viewed as a smoothed version of SignGD, which is the normalized steepest descent with respect to $\ell_\infty$ norm, and a surprising connection between normalized steepest descent with weight decay and Frank-Wolfe.

We study the algorithmic task of finding large independent sets in Erdos-Renyi $r$-uniform hypergraphs on $n$ vertices having average degree $d$. Krivelevich and Sudakov showed that the maximum independent set has density $\left(\frac{r\log d}{(r-1)d}\right)^{1/(r-1)}$. We show that the class of low-degree polynomial algorithms can find independent sets of density $\left(\frac{\log d}{(r-1)d}\right)^{1/(r-1)}$ but no larger. This extends and generalizes earlier results of Gamarnik and Sudan, Rahman and Virag, and Wein on graphs, and answers a question of Bal and Bennett. We conjecture that this statistical-computational gap holds for this problem. Additionally, we explore the universality of this gap by examining $r$-partite hypergraphs. A hypergraph $H=(V,E)$ is $r$-partite if there is a partition $V=V_1\cup\cdots\cup V_r$ such that each edge contains exactly one vertex from each set $V_i$. We consider the problem of finding large balanced independent sets (independent sets containing the same number of vertices in each partition) in random $r$-partite hypergraphs with $n$ vertices in each partition and average degree $d$. We prove that the maximum balanced independent set has density $\left(\frac{r\log d}{(r-1)d}\right)^{1/(r-1)}$ asymptotically. Furthermore, we prove an analogous low-degree computational threshold of $\left(\frac{\log d}{(r-1)d}\right)^{1/(r-1)}$. Our results recover and generalize recent work of Perkins and the second author on bipartite graphs. While the graph case has been extensively studied, this work is the first to consider statistical-computational gaps of optimization problems on random hypergraphs. Our results suggest that these gaps persist for larger uniformities as well as across many models. A somewhat surprising aspect of the gap for balanced independent sets is that the algorithm achieving the lower bound is a simple degree-1 polynomial.

One of today's main concerns is to bring Artificial Intelligence power to embedded systems for edge applications. The hardware resources and power consumption required by state-of-the-art models are incompatible with the constrained environments observed in edge systems, such as IoT nodes and wearable devices. Spiking Neural Networks (SNNs) can represent a solution in this sense: inspired by neuroscience, they reach unparalleled power and resource efficiency when run on dedicated hardware accelerators. However, when designing such accelerators, the amount of choices that can be taken is huge. This paper presents SpikExplorer, a modular and flexible Python tool for hardware-oriented Automatic Design Space Exploration to automate the configuration of FPGA accelerators for SNNs. Using Bayesian optimizations, SpikerExplorer enables hardware-centric multi-objective optimization, supporting factors such as accuracy, area, latency, power, and various combinations during the exploration process. The tool searches the optimal network architecture, neuron model, and internal and training parameters, trying to reach the desired constraints imposed by the user. It allows for a straightforward network configuration, providing the full set of explored points for the user to pick the trade-off that best fits the needs. The potential of SpikExplorer is showcased using three benchmark datasets. It reaches 95.8% accuracy on the MNIST dataset, with a power consumption of 180mW/image and a latency of 0.12 ms/image, making it a powerful tool for automatically optimizing SNNs.

We use the PAC-Bayesian theory for the setting of learning-to-optimize. To the best of our knowledge, we present the first framework to learn optimization algorithms with provable generalization guarantees (PAC-Bayesian bounds) and explicit trade-off between convergence guarantees and convergence speed, which contrasts with the typical worst-case analysis. Our learned optimization algorithms provably outperform related ones derived from a (deterministic) worst-case analysis. The results rely on PAC-Bayesian bounds for general, possibly unbounded loss-functions based on exponential families. Then, we reformulate the learning procedure into a one-dimensional minimization problem and study the possibility to find a global minimum. Furthermore, we provide a concrete algorithmic realization of the framework and new methodologies for learning-to-optimize, and we conduct four practically relevant experiments to support our theory. With this, we showcase that the provided learning framework yields optimization algorithms that provably outperform the state-of-the-art by orders of magnitude.

Before autonomous systems can be deployed in safety-critical applications, we must be able to understand and verify the safety of these systems. For cases where the risk or cost of real-world testing is prohibitive, we propose a simulation-based framework for a) predicting ways in which an autonomous system is likely to fail and b) automatically adjusting the system's design and control policy to preemptively mitigate those failures. Existing tools for failure prediction struggle to search over high-dimensional environmental parameters, cannot efficiently handle end-to-end testing for systems with vision in the loop, and provide little guidance on how to mitigate failures once they are discovered. We approach this problem through the lens of approximate Bayesian inference and use differentiable simulation and rendering for efficient failure case prediction and repair. For cases where a differentiable simulator is not available, we provide a gradient-free version of our algorithm, and we include a theoretical and empirical evaluation of the trade-offs between gradient-based and gradient-free methods. We apply our approach on a range of robotics and control problems, including optimizing search patterns for robot swarms, UAV formation control, and robust network control. Compared to optimization-based falsification methods, our method predicts a more diverse, representative set of failure modes, and we find that our use of differentiable simulation yields solutions that have up to 10x lower cost and requires up to 2x fewer iterations to converge relative to gradient-free techniques. In hardware experiments, we find that repairing control policies using our method leads to a 5x robustness improvement. Accompanying code and video can be found at https://mit-realm.github.io/radium/