So we can check that ddtE(qt,λt) (qt,λt) in both cases. Combing the two cases yield the result. Pm i=1N(θ;µi,σ2i) where m is fixed to5 in all the experiments. Monotonic Bayesian Neural Networks In this experiment, we use the COMPAS dataset (J. The task istopredict whether the individual will commit acrime againin2years.

Real-world systems are often formulated as constrained optimization problems. Techniques to incorporate constraints into Neural Networks (NN), such as Neural Ordinary Differential Equations (Neural ODEs), have been used. However, these introduce hyperparameters that require manual tuning through trial and error, raising doubts about the successful incorporation of constraints into the generated model. This paper describes in detail the two-stage training method for Neural ODEs, a simple, effective, and penalty parameter-free approach to model constrained systems. In this approach the constrained optimization problem is rewritten as two unconstrained sub-problems that are solved in two stages. The first stage aims at finding feasible NN parameters by minimizing a measure of constraints violation. The second stage aims to find the optimal NN parameters by minimizing the loss function while keeping inside the feasible region. We experimentally demonstrate that our method produces models that satisfy the constraints and also improves their predictive performance. Thus, ensuring compliance with critical system properties and also contributing to reducing data quantity requirements. Furthermore, we show that the proposed method improves the convergence to an optimal solution and improves the explainability of Neural ODE models. Our proposed two-stage training method can be used with any NN architectures.

Logic synthesis, a pivotal stage in chip design, entails optimizing chip specifications encoded in hardware description languages like Verilog into highly efficient implementations using Boolean logic gates. The process involves a sequential application of logic minimization heuristics ("synthesis recipe"), with their arrangement significantly impacting crucial metrics such as area and delay. Addressing the challenge posed by the broad spectrum of design complexities -- from variations of past designs (e.g., adders and multipliers) to entirely novel configurations (e.g., innovative processor instructions) -- requires a nuanced'synthesis recipe' guided by human expertise and intuition. This study conducts a thorough examination of learning and search techniques for logic synthesis, unearthing a surprising revelation: pre-trained agents, when confronted with entirely novel designs, may veer off course, detrimentally affecting the search trajectory. We present ABC-RL, a meticulously tuned α parameter that adeptly adjusts recommendations from pre-trained agents during the search process. Computed based on similarity scores through nearest neighbor retrieval from the training dataset, ABC-RL yields superior synthesis recipes tailored for a wide array of hardware designs. Our findings showcase substantial enhancements in the Quality-of-result (QoR) of synthesized circuits, boasting improvements of up to 24.8% compared to state-of-the-art techniques. Furthermore, ABC-RL achieves an impressive up to 9x reduction in runtime (iso-QoR) when compared to current state-of-the-art methodologies. Modern chips are designed using sophisticated electronic design automation (EDA) algorithms that automatically convert logic functions expressed in a hardware description language (HDL) like Verilog to a physical layout that can be manufactured at a semiconductor foundry. EDA involves a sequence of steps, the first of which is logic synthesis. Logic synthesis converts HDL into a low-level "netlist" of Boolean logic gates that implement the desired function. A netlist is a graph whose nodes are logic gates (e.g., ANDs, NOTs, ORs) and whose edges represent connections between gates.

Bayesian optimization is a principled optimization strategy for a black-box objective function. It shows its effectiveness in a wide variety of real-world applications such as scientific discovery and experimental design. In general, the performance of Bayesian optimization is assessed by regret-based metrics such as instantaneous, simple, and cumulative regrets. These metrics only rely on function evaluations, so that they do not consider geometric relationships between query points and global solutions, or query points themselves. Notably, they cannot discriminate if multiple global solutions are successfully found. Moreover, they do not evaluate Bayesian optimization's abilities to exploit and explore a search space given. To tackle these issues, we propose four new geometric metrics, i.e., precision, recall, average degree, and average distance. These metrics allow us to compare Bayesian optimization algorithms considering the geometry of both query points and global optima, or query points. However, they are accompanied by an extra parameter, which needs to be carefully determined. We therefore devise the parameter-free forms of the respective metrics by integrating out the additional parameter. Finally, we empirically validate that our proposed metrics can provide more convincing interpretation and understanding of Bayesian optimization algorithms from distinct perspectives, compared to the conventional metrics.

Bayesian optimization has attracted huge attention from diverse research areas in science and engineering, since it is capable of finding a global optimum of an expensive-to-evaluate black-box function efficiently. In general, a probabilistic regression model, e.g., Gaussian processes and Bayesian neural networks, is widely used as a surrogate function to model an explicit distribution over function evaluations given an input to estimate and a training dataset. Beyond the probabilistic regression-based Bayesian optimization, density ratio estimation-based Bayesian optimization has been suggested in order to estimate a density ratio of the groups relatively close and relatively far to a global optimum. Developing this line of research further, a supervised classifier can be employed to estimate a class probability for the two groups instead of a density ratio. However, the supervised classifiers used in this strategy are prone to be overconfident for a global solution candidate. To solve this problem, we propose density ratio estimation-based Bayesian optimization with semi-supervised learning. Finally, we demonstrate the experimental results of our methods and several baseline methods in two distinct scenarios with unlabeled point sampling and a fixed-size pool. Bayesian optimization (Brochu et al., 2010; Garnett, 2023) has attracted immense attention from various research areas such as hyperparameter optimization (Bergstra et al., 2011), battery lifetime optimization (Attia et al., 2020), and chemical reaction optimization (Shields et al., 2021), since it is capable of finding a global optimum of an expensive-to-evaluate black-box function in a sampleefficient manner. As studied in previous literature on Bayesian optimization (Snoek et al., 2012; Martinez-Cantin et al., 2018; Springenberg et al., 2016; Hutter et al., 2011), a probabilistic regression model, which can estimate a distribution of function evaluations over inputs, is widely used as a surrogate function; Gaussian process (GP) regression (Rasmussen & Williams, 2006) is a predominant choice for the surrogate function.

Logic synthesis is the first and most vital step in chip design. This steps converts a chip specification written in a hardware description language (such as Verilog) into an optimized implementation using Boolean logic gates. State-of-the-art logic synthesis algorithms have a large number of logic minimization heuristics, typically applied sequentially based on human experience and intuition. The choice of the order greatly impacts the quality (e.g., area and delay) of the synthesized circuit. In this paper, we propose INVICTUS, a model-based offline reinforcement learning (RL) solution that automatically generates a sequence of logic minimization heuristics ("synthesis recipe") based on a training dataset of previously seen designs. A key challenge is that new designs can range from being very similar to past designs (e.g., adders and multipliers) to being completely novel (e.g., new processor instructions). %Compared to prior work, INVICTUS is the first solution that uses a mix of RL and search methods joint with an online out-of-distribution detector to generate synthesis recipes over a wide range of benchmarks. Our results demonstrate significant improvement in area-delay product (ADP) of synthesized circuits with up to 30\% improvement over state-of-the-art techniques. Moreover, INVICTUS achieves up to $6.3\times$ runtime reduction (iso-ADP) compared to the state-of-the-art.

Wind farms are a crucial driver toward the generation of ecological and renewable energy. Due to their rapid increase in capacity, contemporary wind farms need to adhere to strict constraints on power output to ensure stability of the electricity grid. Specifically, a wind farm controller is required to match the farm's power production with a power demand imposed by the grid operator. This is a non-trivial optimization problem, as complex dependencies exist between the wind turbines. State-of-the-art wind farm control typically relies on physics-based heuristics that fail to capture the full load spectrum that defines a turbine's health status. When this is not taken into account, the long-term viability of the farm's turbines is put at risk. Given the complex dependencies that determine a turbine's lifetime, learning a flexible and optimal control strategy requires a data-driven approach. However, as wind farms are large-scale multi-agent systems, optimizing control strategies over the full joint action space is intractable. We propose a new learning method for wind farm control that leverages the sparse wind farm structure to factorize the optimization problem. Using a Bayesian approach, based on multi-agent Thompson sampling, we explore the factored joint action space for configurations that match the demand, while considering the lifetime of turbines. We apply our method to a grid-like wind farm layout, and evaluate configurations using a state-of-the-art wind flow simulator. Our results are competitive with a physics-based heuristic approach in terms of demand error, while, contrary to the heuristic, our method prolongs the lifetime of high-risk turbines.