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.

The deployment of agile autonomous systems in challenging, unstructured environments requires adaptation capabilities and robustness to uncertainties. Existing robust and adaptive controllers, such as those based on model predictive control (MPC), can achieve impressive performance at the cost of heavy online onboard computations. Strategies that efficiently learn robust and onboard-deployable policies from MPC have emerged, but they still lack fundamental adaptation capabilities. In this work, we extend an existing efficient Imitation Learning (IL) algorithm for robust policy learning from MPC with the ability to learn policies that adapt to challenging model/environment uncertainties. The key idea of our approach consists in modifying the IL procedure by conditioning the policy on a learned lower-dimensional model/environment representation that can be efficiently estimated online. We tailor our approach to the task of learning an adaptive position and attitude control policy to track trajectories under challenging disturbances on a multirotor. Evaluations in simulation show that a high-quality adaptive policy can be obtained in about $1.3$ hours. We additionally empirically demonstrate rapid adaptation to in- and out-of-training-distribution uncertainties, achieving a $6.1$ cm average position error under wind disturbances that correspond to about $50\%$ of the weight of the robot, and that are $36\%$ larger than the maximum wind seen during training.

In this paper, we introduce an innovative approach for addressing Bayesian inverse problems through the utilization of physics-informed invertible neural networks (PI-INN). The PI-INN framework encompasses two sub-networks: an invertible neural network (INN) and a neural basis network (NB-Net). The primary role of the NB-Net lies in modeling the spatial basis functions characterizing the solution to the forward problem dictated by the underlying partial differential equation. Simultaneously, the INN is designed to partition the parameter vector linked to the input physical field into two distinct components: the expansion coefficients representing the forward problem solution and the Gaussian latent noise. If the forward mapping is precisely estimated, and the statistical independence between expansion coefficients and latent noise is well-maintained, the PI-INN offers a precise and efficient generative model for Bayesian inverse problems, yielding tractable posterior density estimates. As a particular physics-informed deep learning model, the primary training challenge for PI-INN centers on enforcing the independence constraint, which we tackle by introducing a novel independence loss based on estimated density. We support the efficacy and precision of the proposed PI-INN through a series of numerical experiments, including inverse kinematics, 1-dimensional and 2-dimensional diffusion equations, and seismic traveltime tomography. Specifically, our experimental results showcase the superior performance of the proposed independence loss in comparison to the commonly used but computationally demanding kernel-based maximum mean discrepancy loss.

Many cryptocurrency brokers nowadays offer a variety of derivative assets that allow traders to perform hedging or speculation. This paper proposes an effective algorithm based on neural networks to take advantage of these investment products. The proposed algorithm constructs a portfolio that contains a pair of negatively correlated assets. A deep neural network, which outputs the allocation weight of each asset at a time interval, is trained to maximize the Sharpe ratio. A novel loss term is proposed to regulate the network's bias towards a specific asset, thus enforcing the network to learn an allocation strategy that is close to a minimum variance strategy. Extensive experiments were conducted using data collected from Binance spanning 19 months to evaluate the effectiveness of our approach. The backtest results show that the proposed algorithm can produce neural networks that are able to make profits in different market situations.

Recent work has considered trust-aware decision making for human-robot collaboration (HRC) with a focus on model learning. In this paper, we are interested in enabling the HRC system to complete complex tasks specified using temporal logic that involve human trust. Since human trust in robots is not observable, we adopt the widely used partially observable Markov decision process (POMDP) framework for modelling the interactions between humans and robots. To specify the desired behaviour, we propose to use syntactically co-safe linear distribution temporal logic (scLDTL), a logic that is defined over predicates of states as well as belief states of partially observable systems. The incorporation of belief predicates in scLDTL enhances its expressiveness while simultaneously introducing added complexity. This also presents a new challenge as the belief predicates must be evaluated over the continuous (infinite) belief space. To address this challenge, we present an algorithm for solving the optimal policy synthesis problem. First, we enhance the belief MDP (derived by reformulating the POMDP) with a probabilistic labelling function. Then a product belief MDP is constructed between the probabilistically labelled belief MDP and the automaton translation of the scLDTL formula. Finally, we show that the optimal policy can be obtained by leveraging existing point-based value iteration algorithms with essential modifications. Human subject experiments with 21 participants on a driving simulator demonstrate the effectiveness of the proposed approach.

Time series forecasting presents a significant challenge, particularly when its accuracy relies on external data sources rather than solely on historical values. This issue is prevalent in the financial sector, where the future behavior of time series is often intricately linked to information derived from various textual reports and a multitude of economic indicators. In practice, the key challenge lies in constructing a reliable time series forecasting model capable of harnessing data from diverse sources and extracting valuable insights to predict the target time series accurately. In this work, we tackle this challenging problem and introduce a novel multimodal transformer-based model named the Modality-aware Transformer. Our model excels in exploring the power of both categorical text and numerical timeseries to forecast the target time series effectively while providing insights through its neural attention mechanism. To achieve this, we develop feature-level attention layers that encourage the model to focus on the most relevant features within each data modality. By incorporating the proposed feature-level attention, we develop a novel Intra-modal multi-head attention (MHA), Inter-modal MHA and Modality-target MHA in a way that both feature and temporal attentions are incorporated in MHAs. This enables the MHAs to generate temporal attentions with consideration of modality and feature importance which leads to more informative embeddings. The proposed modality-aware structure enables the model to effectively exploit information within each modality as well as foster cross-modal understanding. Our extensive experiments on financial datasets demonstrate that Modality-aware Transformer outperforms existing methods, offering a novel and practical solution to the complex challenges of multi-modality time series forecasting.

This paper considers the problem of autonomous robot navigation in unknown environments with moving obstacles. We propose a new method that systematically puts planning, motion prediction and safety metric design together to achieve environmental adaptive and safe navigation. This algorithm balances optimality in travel distance and safety with respect to passing clearance. Robot adapts progress speed adaptively according to the sensed environment, being fast in wide open areas and slow down in narrow passages and taking necessary maneuvers to avoid dangerous incoming obstacles. In our method, directional distance measure, conic-shape motion prediction and custom costmap are integrated properly to evaluate system risk accurately with respect to local geometry of surrounding environments. Using such risk estimation, reference governor technique and control barrier function are worked together to enable adaptive and safe path tracking in dynamical environments. We validate our algorithm extensively both in simulation and challenging real-world environments.

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.

Continuous dynamical systems, characterized by differential equations, are ubiquitously used to model several important problems: plasma dynamics, flow through porous media, weather forecasting, and epidemic dynamics. Recently, a wide range of data-driven models has been used successfully to model these systems. However, in contrast to established fields like computer vision, limited studies are available analyzing the strengths and potential applications of different classes of these models that could steer decision-making in scientific machine learning. Here, we introduce CodBench, an exhaustive benchmarking suite comprising 11 state-of-the-art data-driven models for solving differential equations. Specifically, we comprehensively evaluate 4 distinct categories of models, viz., feed forward neural networks, deep operator regression models, frequency-based neural operators, and transformer architectures against 8 widely applicable benchmark datasets encompassing challenges from fluid and solid mechanics. We conduct extensive experiments, assessing the operators' capabilities in learning, zero-shot super-resolution, data efficiency, robustness to noise, and computational efficiency. Interestingly, our findings highlight that current operators struggle with the newer mechanics datasets, motivating the need for more robust neural operators. All the datasets and codes will be shared in an easy-to-use fashion for the scientific community. We hope this resource will be an impetus for accelerated progress and exploration in modeling dynamical systems.