arXiv subjects

Warren B. Powell

Publications and source records attributed to Warren B. Powell.

At least 19 recordsLinked to original sources

arXiv2025

Adaptive Self-Improvement for Smarter Energy Systems using Agentic Policy Search

Controlling energy systems usually involves manually designed policies for decision-making, which can be complex and time-consuming to develop. This process requires interdisciplinary collaboration among multiple domain experts, resulting in slow and inflexible adaptation to rapidly changing environments. Large Language Models (LLMs) offer a promising paradigm shift by integrating extensive contextual knowledge with the capability to generate structured, executable code. We present Agentic Policy Search (APS) -- a novel hierarchical optimization framework in which LLMs act as autonomous agents that propose complete control logics, translate them into executable code, and iteratively improve them through direct system feedback. We apply APS to a residential energy system with PV, battery, demand, and dynamic electricity prices. Within just seven simulated days, the method yields a net profit of up to 6.20 EUR compared to the no-battery reference scenario (-10.70 EUR), nearly matching the global optimum of a perfectly informed linear program. By combining LLM-driven policy search with the generation of human-interpretable control logic, APS effectively bridges adaptability and traceability in energy management -- while also offering a transferable framework for agentic optimization in other domains.

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arXiv2023

Entropy Minimization for Optimization of Expensive, Unimodal Functions

Maximization of an expensive, unimodal function under random observations has been an important problem in hyperparameter tuning. It features expensive function evaluations (which means small budgets) and a high level of noise. We develop an algorithm based on entropy reduction of a probabilistic belief about the optimum. The algorithm provides an efficient way of estimating the computationally intractable surrogate objective in the general Entropy Search algorithm by leveraging a sampled belief model and designing a metric that measures the information value of any search point.

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arXiv2023

The Information-Collecting Vehicle Routing Problem: Stochastic Optimization for Emergency Storm Response

We address the problem of mitigating damage to a power grid following a storm by managing a vehicle that has to be routed while simultaneously performing two tasks: learning about damage from the grid (which requires direct observation) and repairing damage that it observes. The learning process is assisted by calls from customers notifying the utility that they have lost power (``lights-out calls''). However, when a tree falls and damages a line, it triggers the first upstream circuit breaker, which results in power outages for everyone on the grid below the circuit breaker. We present a dynamic routing model that captures observable state variables such as the location of the truck and the state of the grid on segments the truck has visited, and beliefs about outages on segments that have not been visited. Trucks are routed over a physical transportation network, but the pattern of outages is governed by the structure of the power grid. We introduce a form of Monte Carlo tree search based on information relaxation that we call {\it optimistic MCTS} which improves its application to problems with larger action spaces. We show that the method significantly outperforms standard escalation heuristics used in industry.}

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arXiv2022

Stochastic Search for a Parametric Cost Function Approximation: Energy storage with rolling forecasts

Rolling forecasts have been almost overlooked in the renewable energy storage literature. In this paper, we provide a new approach for handling uncertainty not just in the accuracy of a forecast, but in the evolution of forecasts over time. Our approach shifts the focus from modeling the uncertainty in a lookahead model to accurate simulations in a stochastic base model. We develop a robust policy for making energy storage decisions by creating a parametrically modified lookahead model, where the parameters are tuned in the stochastic base model. Since computing unbiased stochastic gradients with respect to the parameters require restrictive assumptions, we propose a simulation-based stochastic approximation algorithm based on numerical derivatives to optimize these parameters. While numerical derivatives, calculated based on the noisy function evaluations, provide biased gradient estimates, an online variance reduction technique built in the framework of our proposed algorithm, will enable us to control the accumulated bias errors and establish the finite-time rate of convergence of the algorithm. Our numerical experiments show the performance of this algorithm in finding policies outperforming the deterministic benchmark policy.

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arXiv2021

Zeroth-order Stochastic Compositional Algorithms for Risk-Aware Learning

We present $\textit{Free-MESSAGE}^{p}$, the first zeroth-order algorithm for (weakly-)convex mean-semideviation-based risk-aware learning, which is also the first three-level zeroth-order compositional stochastic optimization algorithm whatsoever. Using a non-trivial extension of Nesterov's classical results on Gaussian smoothing, we develop the $\textit{Free-MESSAGE}^{p}$ algorithm from first principles, and show that it essentially solves a smoothed surrogate to the original problem, the former being a uniform approximation of the latter, in a useful, convenient sense. We then present a complete analysis of the $\textit{Free-MESSAGE}^{p}$ algorithm, which establishes convergence in a user-tunable neighborhood of the optimal solutions of the original problem for convex costs, as well as explicit convergence rates for convex, weakly convex, and strongly convex costs, and in a unified way. Orderwise, and for fixed problem parameters, our results demonstrate no sacrifice in convergence speed as compared to existing first-order methods, while striking a certain balance among the condition of the problem, its dimensionality, as well as the accuracy of the obtained results, naturally extending previous results in zeroth-order risk-neutral learning.

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arXiv2020

Backward Approximate Dynamic Programming with Hidden Semi-Markov Stochastic Models in Energy Storage Optimization

We consider an energy storage problem involving a wind farm with a forecasted power output, a stochastic load, an energy storage device, and a connection to the larger power grid with stochastic prices. Electricity prices and wind power forecast errors are modeled using a novel hidden semi-Markov model that accurately replicates not just the distribution of the errors, but also crossing times, capturing the amount of time each process stays above or below some benchmark such as the forecast. This is an important property of stochastic processes involved in storage problems. We show that we achieve more robust solutions using this model than when more common stochastic models are considered. The new model introduces some additional complexity to the problem as its information states are partially hidden, forming a partially observable Markov decision process. We derive a near-optimal time-dependent policy using backward approximate dynamic programming, which overcomes the computational hurdles of classical (exact) backward dynamic programming, with higher quality solutions than the more familiar forward approximate dynamic programming methods.

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arXiv2020

Risk Directed Importance Sampling in Stochastic Dual Dynamic Programming with Hidden Markov Models for Grid Level Energy Storage

Power systems that need to integrate renewables at a large scale must account for the high levels of uncertainty introduced by these power sources. This can be accomplished with a system of many distributed grid-level storage devices. However, developing a cost-effective and robust control policy in this setting is a challenge due to the high dimensionality of the resource state and the highly volatile stochastic processes involved. We first model the problem using a carefully calibrated power grid model and a specialized hidden Markov stochastic model for wind power which replicates crossing times. We then base our control policy on a variant of stochastic dual dynamic programming, an algorithm well suited for certain high dimensional control problems, that is modified to accommodate hidden Markov uncertainty in the stochastics. However, the algorithm may be impractical to use as it exhibits relatively slow convergence. To accelerate the algorithm, we apply both quadratic regularization and a risk-directed importance sampling technique for sampling the outcome space at each time step in the backward pass of the algorithm. We show that the resulting policies are more robust than those developed using classical SDDP modeling assumptions and algorithms.

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arXiv2020

Reinforcement Learning via Parametric Cost Function Approximation for Multistage Stochastic Programming

The most common approaches for solving stochastic resource allocation problems in the research literature is to either use value functions ("dynamic programming") or scenario trees ("stochastic programming") to approximate the impact of a decision now on the future. By contrast, common industry practice is to use a deterministic approximation of the future which is easier to understand and solve, but which is criticized for ignoring uncertainty. We show that a parameterized version of a deterministic lookahead can be an effective way of handling uncertainty, while enjoying the computational simplicity of a deterministic lookahead. We present the parameterized lookahead model as a form of policy for solving a stochastic base model, which is used as the basis for optimizing the parameterized policy. This approach can handle complex, high-dimensional state variables, and avoids the usual approximations associated with scenario trees. We formalize this approach and demonstrate its use in the context of a complex, nonstationary energy storage problem.

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arXiv2018

Recursive Optimization of Convex Risk Measures: Mean-Semideviation Models

We develop recursive, data-driven, stochastic subgradient methods for optimizing a new, versatile, and application-driven class of convex risk measures, termed here as mean-semideviations, strictly generalizing the well-known and popular mean-upper-semideviation. We introduce the MESSAGEp algorithm, which is an efficient compositional subgradient procedure for iteratively solving convex mean-semideviation risk-averse problems to optimality. We analyze the asymptotic behavior of the MESSAGEp algorithm under a flexible and structure-exploiting set of problem assumptions. In particular: 1) Under appropriate stepsize rules, we establish pathwise convergence of the MESSAGEp algorithm in a strong technical sense, confirming its asymptotic consistency. 2) Assuming a strongly convex cost, we show that, for fixed semideviation order $p>1$ and for $ε\in\left[0,1\right)$, the MESSAGEp algorithm achieves a squared-${\cal L}_{2}$ solution suboptimality rate of the order of ${\cal O}(n^{-\left(1-ε\right)/2})$ iterations, where, for $ε>0$, pathwise convergence is simultaneously guaranteed. This result establishes a rate of order arbitrarily close to ${\cal O}(n^{-1/2})$, while ensuring strongly stable pathwise operation. For $p\equiv1$, the rate order improves to ${\cal O}(n^{-2/3})$, which also suffices for pathwise convergence, and matches previous results. 3) Likewise, in the general case of a convex cost, we show that, for any $ε\in\left[0,1\right)$, the MESSAGEp algorithm with iterate smoothing achieves an ${\cal L}_{1}$ objective suboptimality rate of the order of ${\cal O}(n^{-\left(1-ε\right)/\left(4\bf{1}_{\left\{ p>1\right\} }+4\right)})$ iterations. This result provides maximal rates of ${\cal O}(n^{-1/4})$, if $p\equiv1$, and ${\cal O}(n^{-1/8})$, if $p>1$, matching the state of the art, as well.

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arXiv2018

Approximate Dynamic Programming for Planning a Ride-Sharing System using Autonomous Fleets of Electric Vehicles

Within a decade, almost every major auto company, along with fleet operators such as Uber, have announced plans to put autonomous vehicles on the road. At the same time, electric vehicles are quickly emerging as a next-generation technology that is cost effective, in addition to offering the benefits of reducing the carbon footprint. The combination of a centrally managed fleet of driverless vehicles, along with the operating characteristics of electric vehicles, is creating a transformative new technology that offers significant cost savings with high service levels. This problem involves a dispatch problem for assigning riders to cars, a surge pricing problem for deciding on the price per trip and a planning problem for deciding on the fleet size. We use approximate dynamic programming to develop high-quality operational dispatch strategies to determine which car is best for a particular trip, when a car should be recharged, and when it should be re-positioned to a different zone which offers a higher density of trips. We prove that the value functions are monotone in the battery and time dimensions and use hierarchical aggregation to get better estimates of the value functions with a small number of observations. Then, surge pricing is discussed using an adaptive learning approach to decide on the price for each trip. Finally, we discuss the fleet size problem which depends on the previous two problems.

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arXiv2017

Practicality of Nested Risk Measures for Dynamic Electric Vehicle Charging

We consider the sequential decision problem faced by the manager of an electric vehicle (EV) charging station, who aims to satisfy the charging demand of the customer while minimizing cost. Since the total time needed to charge the EV up to capacity is often less than the amount of time that the customer is away, there are opportunities to exploit electricity spot price variations within some reservation window. We formulate the problem as a finite horizon Markov decision process (MDP) and consider a risk-averse objective function by optimizing under a dynamic risk measure constructed using a convex combination of expected value and conditional value at risk (CVaR). It has been recognized that the objective function of a risk-averse MDP lacks a practical interpretation. Therefore, in both academic and industry practice, the dynamic risk measure objective is often not of primary interest; instead, the risk-averse MDP is used as a computational tool for solving problems with predefined "practical" risk and reward objectives (termed the base model). In this paper, we study the extent to which the two sides of this framework are compatible with each other for the EV setting -- roughly speaking, does a "more risk-averse" MDP provide lower risk in the practical sense as well? In order to answer such a question, the effect of the degree of dynamic risk-aversion on the optimal MDP policy is analyzed. Based on these results, we also propose a principled approximation approach to finding an instance of the risk-averse MDP whose optimal policy behaves well under the practical objectives of the base model. Our numerical experiments suggest that EV charging stations can be operated at a significantly higher level of profitability if dynamic charging is adopted and a small amount of risk is tolerated.

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arXiv2017

Risk-Averse Approximate Dynamic Programming with Quantile-Based Risk Measures

In this paper, we consider a finite-horizon Markov decision process (MDP) for which the objective at each stage is to minimize a quantile-based risk measure (QBRM) of the sequence of future costs; we call the overall objective a dynamic quantile-based risk measure (DQBRM). In particular, we consider optimizing dynamic risk measures where the one-step risk measures are QBRMs, a class of risk measures that includes the popular value at risk (VaR) and the conditional value at risk (CVaR). Although there is considerable theoretical development of risk-averse MDPs in the literature, the computational challenges have not been explored as thoroughly. We propose data-driven and simulation-based approximate dynamic programming (ADP) algorithms to solve the risk-averse sequential decision problem. We address the issue of inefficient sampling for risk applications in simulated settings and present a procedure, based on importance sampling, to direct samples toward the "risky region" as the ADP algorithm progresses. Finally, we show numerical results of our algorithms in the context of an application involving risk-averse bidding for energy storage.

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arXiv2017

Monte Carlo Tree Search with Sampled Information Relaxation Dual Bounds

Monte Carlo Tree Search (MCTS), most famously used in game-play artificial intelligence (e.g., the game of Go), is a well-known strategy for constructing approximate solutions to sequential decision problems. Its primary innovation is the use of a heuristic, known as a default policy, to obtain Monte Carlo estimates of downstream values for states in a decision tree. This information is used to iteratively expand the tree towards regions of states and actions that an optimal policy might visit. However, to guarantee convergence to the optimal action, MCTS requires the entire tree to be expanded asymptotically. In this paper, we propose a new technique called Primal-Dual MCTS that utilizes sampled information relaxation upper bounds on potential actions, creating the possibility of "ignoring" parts of the tree that stem from highly suboptimal choices. This allows us to prove that despite converging to a partial decision tree in the limit, the recommended action from Primal-Dual MCTS is optimal. The new approach shows significant promise when used to optimize the behavior of a single driver navigating a graph while operating on a ride-sharing platform. Numerical experiments on a real dataset of 7,000 trips in New Jersey suggest that Primal-Dual MCTS improves upon standard MCTS by producing deeper decision trees and exhibits a reduced sensitivity to the size of the action space.

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arXiv2017

Stochastic Optimization with Parametric Cost Function Approximations

A widely used heuristic for solving stochastic optimization problems is to use a deterministic rolling horizon procedure, which has been modified to handle uncertainty (e.g. buffer stocks, schedule slack). This approach has been criticized for its use of a deterministic approximation of a stochastic problem, which is the major motivation for stochastic programming. We recast this debate by identifying both deterministic and stochastic approaches as policies for solving a stochastic base model, which may be a simulator or the real world. Stochastic lookahead models (stochastic programming) require a range of approximations to keep the problem tractable. By contrast, so-called deterministic models are actually parametrically modified cost function approximations which use parametric adjustments to the objective function and/or the constraints. These parameters are then optimized in a stochastic base model which does not require making any of the types of simplifications required by stochastic programming. We formalize this strategy and describe a gradient-based stochastic search strategy to optimize the parameters.

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arXiv2017

Regularized Decomposition of High-Dimensional Multistage Stochastic Programs with Markov Uncertainty

We develop a quadratic regularization approach for the solution of high-dimensional multistage stochastic optimization problems characterized by a potentially large number of time periods/stages (e.g. hundreds), a high-dimensional resource state variable, and a Markov information process. The resulting algorithms are shown to converge to an optimal policy after a finite number of iterations under mild technical assumptions. Computational experiments are conducted using the setting of optimizing energy storage over a large transmission grid, which motivates both the spatial and temporal dimensions of our problem. Our numerical results indicate that the proposed methods exhibit significantly faster convergence than their classical counterparts, with greater gains observed for higher-dimensional problems.

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arXiv2016

Optimal Learning for Stochastic Optimization with Nonlinear Parametric Belief Models

We consider the problem of estimating the expected value of information (the knowledge gradient) for Bayesian learning problems where the belief model is nonlinear in the parameters. Our goal is to maximize some metric, while simultaneously learning the unknown parameters of the nonlinear belief model, by guiding a sequential experimentation process which is expensive. We overcome the problem of computing the expected value of an experiment, which is computationally intractable, by using a sampled approximation, which helps to guide experiments but does not provide an accurate estimate of the unknown parameters. We then introduce a resampling process which allows the sampled model to adapt to new information, exploiting past experiments. We show theoretically that the method converges asymptotically to the true parameters, while simultaneously maximizing our metric. We show empirically that the process exhibits rapid convergence, yielding good results with a very small number of experiments.

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arXiv2016

The Information-Collecting Vehicle Routing Problem: Stochastic Optimization for Emergency Storm Response

Utilities face the challenge of responding to power outages due to storms and ice damage, but most power grids are not equipped with sensors to pinpoint the precise location of the faults causing the outage. Instead, utilities have to depend primarily on phone calls (trouble calls) from customers who have lost power to guide the dispatching of utility trucks. In this paper, we develop a policy that routes a utility truck to restore outages in the power grid as quickly as possible, using phone calls to create beliefs about outages, but also using utility trucks as a mechanism for collecting additional information. This means that routing decisions change not only the physical state of the truck (as it moves from one location to another) and the grid (as the truck performs repairs), but also our belief about the network, creating the first stochastic vehicle routing problem that explicitly models information collection and belief modeling. We address the problem of managing a single utility truck, which we start by formulating as a sequential stochastic optimization model which captures our belief about the state of the grid. We propose a stochastic lookahead policy, and use Monte Carlo tree search (MCTS) to produce a practical policy that is asymptotically optimal. Simulation results show that the developed policy restores the power grid much faster compared to standard industry heuristics.

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arXiv2016

SDDP vs. ADP: The Effect of Dimensionality in Multistage Stochastic Optimization for Grid Level Energy Storage

There has been widespread interest in the use of grid-level storage to handle the variability from increasing penetrations of wind and solar energy. This problem setting requires optimizing energy storage and release decisions for anywhere from a half-dozen, to potentially hundreds of storage devices spread around the grid as new technologies evolve. We approach this problem using two competing algorithmic strategies. The first, developed within the stochastic programming literature, is stochastic dual dynamic programming (SDDP) which uses Benders decomposition to create a multidimensional value function approximations, which have been widely used to manage hydro reservoirs. The second approach, which has evolved using the language of approximate dynamic programming, uses separable, piecewise linear value function approximations, a method which has been successfully applied to high-dimensional fleet management problems. This paper brings these two approaches together using a common notational system, and contrasts the algorithmic strategies (which are both a form of approximate dynamic programming) used by each approach. The methods are then subjected to rigorous testing using the context of optimizing grid level storage.

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