A popular approach to sample a diffusion-based generative model is to solve an ordinary differential equation (ODE). In existing samplers, the coefficients of the ODE solvers are pre-determined by the ODE formulation, the reverse discrete timesteps, and the employed ODE methods. In this paper, we consider accelerating several popular ODE-based sampling processes (including EDM, DDIM, and DPM-Solver) by optimizing certain coefficients via improved integration approximation (IIA). We propose to minimize, for each time step, a mean squared error (MSE) function with respect to the selected coefficients. The MSE is constructed by applying the original ODE solver for a set of fine-grained timesteps, which in principle provides a more accurate integration approximation in predicting the next diffusion state. The proposed IIA technique does not require any change of a pre-trained model, and only introduces a very small computational overhead for solving a number of quadratic optimization problems. Extensive experiments show that considerably better FID scores can be achieved by using IIA-EDM, IIA-DDIM, and IIA-DPM-Solver than the original counterparts when the neural function evaluation (NFE) is small (i.e., less than 25).

Several recent advances in AI systems (e.g., Tree-of-Thoughts and Program-Aided Language Models) solve problems by providing a "scaffolding" program that structures multiple calls to language models to generate better outputs. A scaffolding program is written in a programming language such as Python. In this work, we use a language-model-infused scaffolding program to improve itself. We start with a seed "improver" that improves an input program according to a given utility function by querying a language model several times and returning the best solution. We then run this seed improver to improve itself. Across a small set of downstream tasks, the resulting improved improver generates programs with significantly better performance than its seed improver. A variety of self-improvement strategies are proposed by the language model, including beam search, genetic algorithms, and simulated annealing. Since the language models themselves are not altered, this is not full recursive self-improvement. Nonetheless, it demonstrates that a modern language model, GPT-4 in our proof-of-concept experiments, is capable of writing code that can call itself to improve itself. We consider concerns around the development of self-improving technologies and evaluate the frequency with which the generated code bypasses a sandbox. A language model can be queried to optimize virtually any objective describable in natural language. However, a program that makes multiple, structured calls to a language model can often produce outputs with higher objective values (Yao et al., 2022; 2023; Zelikman et al., 2023; Chen et al., 2022). We refer to these as "scaffolding" programs, typically written (by humans) in a programming language such as Python. Our key observation is that, for any distribution over optimization problems and any fixed language model, the design of a scaffolding program is itself an optimization problem. In this work, we introduce the Self-Taught Optimizer (STOP), a method in which code that applies a language model to improve arbitrary solutions is applied recursively to improve itself. Our approach begins with an initial seed'improver' scaffolding program that uses the language model to improve a solution to some downstream task.

Preference-based optimization algorithms are iterative procedures that seek the optimal calibration of a decision vector based only on comparisons between couples of different tunings. At each iteration, a human decision-maker expresses a preference between two calibrations (samples), highlighting which one, if any, is better than the other. The optimization procedure must use the observed preferences to find the tuning of the decision vector that is most preferred by the decision-maker, while also minimizing the number of comparisons. In this work, we formulate the preference-based optimization problem from a utility theory perspective. Then, we propose GLISp-r, an extension of a recent preference-based optimization procedure called GLISp. The latter uses a Radial Basis Function surrogate to describe the tastes of the decision-maker. Iteratively, GLISp proposes new samples to compare with the best calibration available by trading off exploitation of the surrogate model and exploration of the decision space. In GLISp-r, we propose a different criterion to use when looking for new candidate samples that is inspired by MSRS, a popular procedure in the black-box optimization framework. Compared to GLISp, GLISp-r is less likely to get stuck on local optima of the preference-based optimization problem. We motivate this claim theoretically, with a proof of global convergence, and empirically, by comparing the performances of GLISp and GLISp-r on several benchmark optimization problems.

We consider a gossip network, consisting of $n$ nodes, which tracks the information at a source. The source updates its information with a Poisson arrival process and also sends updates to the nodes in the network. The nodes themselves can exchange information among themselves to become as timely as possible. However, the network structure is sparse and irregular, i.e., not every node is connected to every other node in the network, rather, the order of connectivity is low, and varies across different nodes. This asymmetry of the network implies that the nodes in the network do not perform equally in terms of timelines. Due to the gossiping nature of the network, some nodes are able to track the source very timely, whereas, some nodes fall behind versions quite often. In this work, we investigate how the rate-constrained source should distribute its update rate across the network to maintain fairness regarding timeliness, i.e., the overall worst case performance of the network can be minimized. Due to the continuous search space for optimum rate allocation, we formulate this problem as a continuum-armed bandit problem and employ Gaussian process based Bayesian optimization to meet a trade-off between exploration and exploitation sequentially.

In this paper, we present a differentiable, decision-oriented learning technique for a class of vehicle routing problems. Specifically, we consider a scenario where a team of Unmanned Aerial Vehicles (UAVs) and Unmanned Ground Vehicles (UGVs) are persistently monitoring an environment. The UGVs are occasionally taken over by humans to take detours to recharge the depleted UAVs. The goal is to select routes for the UGVs so that they can efficiently monitor the environment while reducing the cost of interventions. The former is modeled as a monotone, submodular function whereas the latter is a linear function of the routes of the UGVs. We consider a scenario where the former is known but the latter depends on the context (e.g., wind and terrain conditions) that must be learned. Typically, we first learn to predict the cost function and then solve the optimization problem. However, the loss function used in prediction may be misaligned with our final goal of finding good routes. We propose a \emph{decision-oriented learning} framework that incorporates task optimization as a differentiable layer in the prediction phase. To make the task optimization (which is a non-monotone submodular function) differentiable, we propose the Differentiable Cost Scaled Greedy algorithm. We demonstrate the efficacy of the proposed framework through numerical simulations. The results show that the proposed framework can result in better performance than the traditional approach.

The challenge of finding a global optimum in a solution search space with limited resources and higher accuracy has given rise to several optimization algorithms. Generally, the gradient-based optimizers converge to the global solution very accurately, but they often require a large number of iterations to find the solution. Researchers took inspiration from different natural phenomena and behaviours of many living organisms to develop algorithms that can solve optimization problems much quicker with high accuracy. These algorithms are called nature-inspired meta-heuristic optimization algorithms. These can be used for denoising signals, updating weights in a deep neural network, and many other cases. In the state-of-the-art, there are no systematic reviews available that have discussed the applications of nature-inspired algorithms on biomedical signal processing. The paper solves that gap by discussing the applications of such algorithms in biomedical signal processing and also provides an updated survey of the application of these algorithms in biomedical image processing. The paper reviews 28 latest peer-reviewed relevant articles and 26 nature-inspired algorithms and segregates them into thoroughly explored, lesser explored and unexplored categories intending to help readers understand the reliability and exploration stage of each of these algorithms.

Reactive trajectory optimization for robotics presents formidable challenges, demanding the rapid generation of purposeful robot motion in complex and swiftly changing dynamic environments. While much existing research predominantly addresses robotic motion planning with predefined objectives, emerging problems in robotic trajectory optimization frequently involve dynamically evolving objectives and stochastic motion dynamics. However, effectively addressing such reactive trajectory optimization challenges for robot manipulators proves difficult due to inefficient, high-dimensional trajectory representations and a lack of consideration for time optimization. In response, we introduce a novel trajectory optimization framework called RETRO. RETRO employs adaptive optimization techniques that span both spatial and temporal dimensions. As a result, it achieves a remarkable computing complexity of $O(T^{2.4}) + O(Tn^{2})$, a significant improvement over the traditional application of DDP, which leads to a complexity of $O(n^{4})$ when reasonable time step sizes are used. To evaluate RETRO's performance in terms of error, we conducted a comprehensive analysis of its regret bounds, comparing it to an Oracle value function obtained through an Oracle trajectory optimization algorithm. Our analytical findings demonstrate that RETRO's total regret can be upper-bounded by a function of the chosen time step size. Moreover, our approach delivers smoothly optimized robot trajectories within the joint space, offering flexibility and adaptability for various tasks. It can seamlessly integrate task-specific requirements such as collision avoidance while maintaining real-time control rates. We validate the effectiveness of our framework through extensive simulations and real-world robot experiments in closed-loop manipulation scenarios.

The Quadratic Assignment Problem (QAP) is an NP-hard problem which has proven particularly challenging to solve: unlike other combinatorial problems like the traveling salesman problem (TSP), which can be solved to optimality for instances with hundreds or even thousands of locations using advanced integer programming techniques, no methods are known to exactly solve QAP instances of size greater than 30. Solving the QAP is nevertheless important because of its many critical applications, such as electronic wiring design and facility layout selection. We propose a method to solve the original Koopmans-Beckman formulation of the QAP using deep reinforcement learning. Our approach relies on a novel double pointer network, which alternates between selecting a location in which to place the next facility and a facility to place in the previous location. We train our model using A2C on a large dataset of synthetic instances, producing solutions with no instance-specific retraining necessary. Out of sample, our solutions are on average within 7.5% of a high-quality local search baseline, and even outperform it on 1.2% of instances.

Gray-box models offer significant benefit over black-box approaches for equipment emulator development for equipment since their integration of physics provides more confidence in the model outside of the training domain. However, challenges such as model nonlinearity, unmodeled dynamics, and local minima introduce uncertainties into grey-box creation that contemporary approaches have failed to overcome, leading to their under-performance compared with black-box models. This paper seeks to address these uncertainties by injecting noise into the training dataset. This noise injection enriches the dataset and provides a measure of robustness against such uncertainties. A dynamic model for a water-to-water heat exchanger has been used as a demonstration case for this approach and tested using a pair of real devices with live data streaming. Compared to the unprocessed signal data, the application of noise injection resulted in a significant reduction in modeling error (root mean square error), decreasing from 0.68 to 0.27{\deg}C. This improvement amounts to a 60% enhancement when assessed on the training set, and improvements of 50% and 45% when validated against the test and validation sets, respectively.

Tracking and modeling unknown rigid objects in the environment play a crucial role in autonomous unmanned systems and virtual-real interactive applications. However, many existing Simultaneous Localization, Mapping and Moving Object Tracking (SLAMMOT) methods focus solely on estimating specific object poses and lack estimation of object scales and are unable to effectively track unknown objects. In this paper, we propose a novel SLAM backend that unifies ego-motion tracking, rigid object motion tracking, and modeling within a joint optimization framework. In the perception part, we designed a pixel-level asynchronous object tracker (AOT) based on the Segment Anything Model (SAM) and DeAOT, enabling the tracker to effectively track target unknown objects guided by various predefined tasks and prompts. In the modeling part, we present a novel object-centric quadric parameterization to unify both static and dynamic object initialization and optimization. Subsequently, in the part of object state estimation, we propose a tightly coupled optimization model for object pose and scale estimation, incorporating hybrids constraints into a novel dual sliding window optimization framework for joint estimation. To our knowledge, we are the first to tightly couple object pose tracking with light-weight modeling of dynamic and static objects using quadric. We conduct qualitative and quantitative experiments on simulation datasets and real-world datasets, demonstrating the state-of-the-art robustness and accuracy in motion estimation and modeling. Our system showcases the potential application of object perception in complex dynamic scenes.