Numerous challenges in science and engineering can be framed as optimization tasks, including the maximization of reaction yields, the optimization of molecular and materials properties, and the fine-tuning of automated hardware protocols. Design of experiment and optimization algorithms are often adopted to solve these tasks efficiently. Increasingly, these experiment planning strategies are coupled with automated hardware to enable autonomous experimental platforms. The vast majority of the strategies used, however, do not consider robustness against the variability of experiment and process conditions. In fact, it is generally assumed that these parameters are exact and reproducible. Yet some experiments may have considerable noise associated with some of their conditions, and process parameters optimized under precise control may be applied in the future under variable operating conditions. In either scenario, the optimal solutions found might not be robust against input variability, affecting the reproducibility of results and returning suboptimal performance in practice. Here, we introduce Golem, an algorithm that is agnostic to the choice of experiment planning strategy and that enables robust experiment and process optimization. Golem identifies optimal solutions that are robust to input uncertainty, thus ensuring the reproducible performance of optimized experimental protocols and processes. It can be used to analyze the robustness of past experiments, or to guide experiment planning algorithms toward robust solutions on the fly. We assess the performance and domain of applicability of Golem through extensive benchmark studies and demonstrate its practical relevance by optimizing an analytical chemistry protocol under the presence of significant noise in its experimental conditions.
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Integer programs provide a powerful abstraction for representing a wide range of real-world scheduling problems. Despite their ability to model general scheduling problems, solving large-scale integer programs (IP) remains a computational challenge in practice. The incorporation of more complex objectives such as robustness to disruptions further exacerbates the computational challenge. We present NICE (Neural network IP Coefficient Extraction), a novel technique that combines reinforcement learning and integer programming to tackle the problem of robust scheduling. More specifically, NICE uses reinforcement learning to approximately represent complex objectives in an integer programming formulation. We use NICE to determine assignments of pilots to a flight crew schedule so as to reduce the impact of disruptions. We compare NICE with (1) a baseline integer programming formulation that produces a feasible crew schedule, and (2) a robust integer programming formulation that explicitly tries to minimize the impact of disruptions. Our experiments show that, across a variety of scenarios, NICE produces schedules resulting in 33\% to 48\% fewer disruptions than the baseline formulation. Moreover, in more severely constrained scheduling scenarios in which the robust integer program fails to produce a schedule within 90 minutes, NICE is able to build robust schedules in less than 2 seconds on average.
Coverage of an inaccessible or challenging region with potential health and safety hazards, such as in a volcanic region, is difficult yet crucial from scientific and meteorological perspectives. Areas contained within the region often provide valuable information of varying importance. We present an algorithm to optimally cover a volcanic region in Hawai`i with an unmanned aerial vehicle (UAV). The target region is assigned with a nonuniform coverage importance score distribution. For a specified battery capacity of the UAV, the optimization problem seeks the path that maximizes the total coverage area and the accumulated importance score while penalizing the revisiting of the same area. Trajectories are generated offline for the UAV based on the available power and coverage information map. The optimal trajectory minimizes the unspent battery power while enforcing that the UAV returns to its starting location. This multi-objective optimization problem is solved by using sequential quadratic programming. The details of the competitive optimization problem are discussed along with the analysis and simulation results to demonstrate the applicability of the proposed algorithm.
Stochastic gradient descent with momentum (SGDM) is the dominant algorithm in many optimization scenarios, including convex optimization instances and non-convex neural network training. Yet, in the stochastic setting, momentum interferes with gradient noise, often leading to specific step size and momentum choices in order to guarantee convergence, set aside acceleration. Proximal point methods, on the other hand, have gained much attention due to their numerical stability and elasticity against imperfect tuning. Their stochastic accelerated variants though have received limited attention: how momentum interacts with the stability of (stochastic) proximal point methods remains largely unstudied. To address this, we focus on the convergence and stability of the stochastic proximal point algorithm with momentum (SPPAM), and show that SPPAM allows a faster linear convergence to a neighborhood compared to stochastic proximal point algorithm (SPPA) with a better contraction factor, under proper hyperparameter tuning. In terms of stability, we show that SPPAM depends on problem constants more favorably than SGDM, allowing a wider range of step size and momentum that lead to convergence.
In many practical applications of RL, it is expensive to observe state transitions from the environment. For example, in the problem of plasma control for nuclear fusion, computing the next state for a given state-action pair requires querying an expensive transition function which can lead to many hours of computer simulation or dollars of scientific research. Such expensive data collection prohibits application of standard RL algorithms which usually require a large number of observations to learn. In this work, we address the problem of efficiently learning a policy while making a minimal number of state-action queries to the transition function. In particular, we leverage ideas from Bayesian optimal experimental design to guide the selection of state-action queries for efficient learning. We propose an acquisition function that quantifies how much information a state-action pair would provide about the optimal solution to a Markov decision process. At each iteration, our algorithm maximizes this acquisition function, to choose the most informative state-action pair to be queried, thus yielding a data-efficient RL approach. We experiment with a variety of simulated continuous control problems and show that our approach learns an optimal policy with up to $5$ -- $1,000\times$ less data than model-based RL baselines and $10^3$ -- $10^5\times$ less data than model-free RL baselines. We also provide several ablated comparisons which point to substantial improvements arising from the principled method of obtaining data.
In this paper, pragmatic implementation of an indoor autonomous delivery system that exploits Reinforcement Learning algorithms for path planning and collision avoidance is audited. The proposed system is a cost-efficient approach that is implemented to facilitate a Raspberry Pi controlled four-wheel-drive non-holonomic robot map a grid. This approach computes and navigates the shortest path from a source key point to a destination key point to carry out the desired delivery. Q learning and Deep-Q learning are used to find the optimal path while avoiding collision with static obstacles. This work defines an approach to deploy these two algorithms on a robot. A novel algorithm to decode an array of directions into accurate movements in a certain action space is also proposed. The procedure followed to dispatch this system with the said requirements is described, ergo presenting our proof of concept for indoor autonomous delivery vehicles.
Reinforcement Learning (RL) controllers have generated excitement within the control community. The primary advantage of RL controllers relative to existing methods is their ability to optimize uncertain systems independently of explicit assumption of process uncertainty. Recent focus on engineering applications has been directed towards the development of safe RL controllers. Previous works have proposed approaches to account for constraint satisfaction through constraint tightening from the domain of stochastic model predictive control. Here, we extend these approaches to account for plant-model mismatch. Specifically, we propose a data-driven approach that utilizes Gaussian processes for the offline simulation model and use the associated posterior uncertainty prediction to account for joint chance constraints and plant-model mismatch. The method is benchmarked against nonlinear model predictive control via case studies. The results demonstrate the ability of the methodology to account for process uncertainty, enabling satisfaction of joint chance constraints even in the presence of plant-model mismatch.
Optimization of hyperparameters of Gaussian process regression (GPR) determines success or failure of the application of the method. Such optimization is difficult with sparse data, in particular in high-dimensional spaces where the data sparsity issue cannot be resolved by adding more data. We show that parameter optimization is facilitated by rectangularization of the defining equation of GPR. On the example of a 15-dimensional molecular potential energy surface we demonstrate that this approach allows effective hyperparameter tuning even with very sparse data.
Reinforcement learning has lead to considerable break-throughs in diverse areas such as robotics, games and many others. But the application to RL in complex real-world decision making problems remains limited. Many problems in operations management (inventory and revenue management, for example) are characterized by large action spaces and stochastic system dynamics. These characteristics make the problem considerably harder to solve for existing RL methods that rely on enumeration techniques to solve per step action problems. To resolve these issues, we develop Programmable Actor Reinforcement Learning (PARL), a policy iteration method that uses techniques from integer programming and sample average approximation. Analytically, we show that the for a given critic, the learned policy in each iteration converges to the optimal policy as the underlying samples of the uncertainty go to infinity. Practically, we show that a properly selected discretization of the underlying uncertain distribution can yield near optimal actor policy even with very few samples from the underlying uncertainty. We then apply our algorithm to real-world inventory management problems with complex supply chain structures and show that PARL outperforms state-of-the-art RL and inventory optimization methods in these settings. We find that PARL outperforms commonly used base stock heuristic by 44.7% and the best performing RL method by up to 12.1% on average across different supply chain environments.
The difficulty in specifying rewards for many real-world problems has led to an increased focus on learning rewards from human feedback, such as demonstrations. However, there are often many different reward functions that explain the human feedback, leaving agents with uncertainty over what the true reward function is. While most policy optimization approaches handle this uncertainty by optimizing for expected performance, many applications demand risk-averse behavior. We derive a novel policy gradient-style robust optimization approach, PG-BROIL, that optimizes a soft-robust objective that balances expected performance and risk. To the best of our knowledge, PG-BROIL is the first policy optimization algorithm robust to a distribution of reward hypotheses which can scale to continuous MDPs. Results suggest that PG-BROIL can produce a family of behaviors ranging from risk-neutral to risk-averse and outperforms state-of-the-art imitation learning algorithms when learning from ambiguous demonstrations by hedging against uncertainty, rather than seeking to uniquely identify the demonstrator's reward function.
Robust estimation is much more challenging in high dimensions than it is in one dimension: Most techniques either lead to intractable optimization problems or estimators that can tolerate only a tiny fraction of errors. Recent work in theoretical computer science has shown that, in appropriate distributional models, it is possible to robustly estimate the mean and covariance with polynomial time algorithms that can tolerate a constant fraction of corruptions, independent of the dimension. However, the sample and time complexity of these algorithms is prohibitively large for high-dimensional applications. In this work, we address both of these issues by establishing sample complexity bounds that are optimal, up to logarithmic factors, as well as giving various refinements that allow the algorithms to tolerate a much larger fraction of corruptions. Finally, we show on both synthetic and real data that our algorithms have state-of-the-art performance and suddenly make high-dimensional robust estimation a realistic possibility.
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