arXiv subjects

Nathan Dahlin

Publications and source records attributed to Nathan Dahlin.

15 recordsLinked to original sources

arXiv2026

Risk-Aware Hosting Capacity Analysis for Flexible Load Interconnection in Distribution Networks

The increasing penetration of flexible loads, such as electric vehicles and AI data-centers necessitates new methodologies for quantifying electrical load hosting capacity under operational constraints and flexible connection agreements. We propose a risk-aware hosting capacity framework that explicitly accounts for both flexibility, in the form of load curtailment, and system reliability. The proposed method incorporates a Conditional Value-at-Risk (CVaR) constraint to control the tail risk of excessive curtailment, ensuring that extreme interventions remain limited. Additionally, a weighted $\ell_1$ approach is introduced to limit the number of utility-controlled interventions, enabling control over the frequency of curtailment actions. A regularization parameter is used to tune the intervention count to a desired intervention budget. The resulting optimization formulation is convex and efficiently solvable, allowing scalable implementation. Numerical results demonstrate that the proposed method significantly increases hosting capacity while maintaining strict risk guarantees and limiting intervention frequency, providing a practical balance between flexibility and reliability in distribution systems.

eess.SY↗

arXiv2025

Sustainable Grid through Distributed Data Centers: Spinning AI Demand for Grid Stabilization and Optimization

We propose a disruptive paradigm to actively place and schedule TWhrs of parallel AI jobs strategically on the grid, at distributed, grid-aware high performance compute data centers (HPC) capable of using their massive power and energy load to stabilize the grid while reducing grid build-out requirements, maximizing use of renewable energy, and reducing Green House Gas (GHG) emissions. Our approach will enable the creation of new, value adding markets for spinning compute demand, providing market based incentives that will drive the joint optimization of energy and learning.

cs.DC↗

arXiv2025

Risk-Sensitive Security-Constrained Economic Dispatch: Pricing and Algorithm Design

We propose a risk-sensitive security-constrained economic dispatch (R-SCED) formulation capturing the tradeoff between dispatch cost and resilience against potential line failures, where risk is modeled via the conditional value at risk (CVaR). In the context of our formulation, we analyze revenue adequacy and side payments of two pricing models, one based on nominal generation costs, and another based on total marginal cost including contingencies. In particular, we prove that the system operator's (SO) merchandising surplus (MS) and total revenue are nonnegative under the latter, while under the former the same does not hold in general. We demonstrate that the proposed R-SCED formulation is amenable to decomposition and describe a Benders' decomposition algorithm to solve it. In numerical examples, we illustrate the differences in MS and total revenue under the considered pricing schemes, and the computational efficiency of our decomposition approach.

eess.SY↗

arXiv2025

Nonparametric Sparse Online Learning of the Koopman Operator

The Koopman operator provides a powerful framework for representing the dynamics of general nonlinear dynamical systems. Data-driven techniques to learn the Koopman operator typically assume that the chosen function space is closed under system dynamics. In this paper, we study the Koopman operator via its action on the reproducing kernel Hilbert space (RKHS), and explore the mis-specified scenario where the dynamics may escape the chosen function space. We relate the Koopman operator to the conditional mean embeddings (CME) operator and then present an operator stochastic approximation algorithm to learn the Koopman operator iteratively with control over the complexity of the representation. We provide both asymptotic and finite-time last-iterate guarantees of the online sparse learning algorithm with trajectory-based sampling with an analysis that is substantially more involved than that for finite-dimensional stochastic approximation. Numerical examples confirm the effectiveness of the proposed algorithm.

stat.ML↗

arXiv2024

Markov Balance Satisfaction Improves Performance in Strictly Batch Offline Imitation Learning

Imitation learning (IL) is notably effective for robotic tasks where directly programming behaviors or defining optimal control costs is challenging. In this work, we address a scenario where the imitator relies solely on observed behavior and cannot make environmental interactions during learning. It does not have additional supplementary datasets beyond the expert's dataset nor any information about the transition dynamics. Unlike state-of-the-art (SOTA) IL methods, this approach tackles the limitations of conventional IL by operating in a more constrained and realistic setting. Our method uses the Markov balance equation and introduces a novel conditional density estimation-based imitation learning framework. It employs conditional normalizing flows for transition dynamics estimation and aims at satisfying a balance equation for the environment. Through a series of numerical experiments on Classic Control and MuJoCo environments, we demonstrate consistently superior empirical performance compared to many SOTA IL algorithms.

cs.LG↗

arXiv2024

Nonparametric Sparse Online Learning of the Koopman Operator

The Koopman operator provides a powerful framework for representing the dynamics of general nonlinear dynamical systems. However, existing data-driven approaches to learning the Koopman operator rely on batch data. In this work, we present a sparse online learning algorithm that learns the Koopman operator iteratively via stochastic approximation, with explicit control over model complexity and provable convergence guarantees. Specifically, we study the Koopman operator via its action on the reproducing kernel Hilbert space (RKHS), and address the mis-specified scenario where the dynamics may escape the chosen RKHS. In this mis-specified setting, we relate the Koopman operator to the conditional mean embeddings (CME) operator. We further establish both asymptotic and finite-time convergence guarantees for our learning algorithm in mis-specified setting, with trajectory-based sampling where the data arrive sequentially over time. Numerical experiments demonstrate the algorithm's capability to learn unknown nonlinear dynamics.

stat.ML↗

arXiv2023

Conditional Kernel Imitation Learning for Continuous State Environments

Imitation Learning (IL) is an important paradigm within the broader reinforcement learning (RL) methodology. Unlike most of RL, it does not assume availability of reward-feedback. Reward inference and shaping are known to be difficult and error-prone methods particularly when the demonstration data comes from human experts. Classical methods such as behavioral cloning and inverse reinforcement learning are highly sensitive to estimation errors, a problem that is particularly acute in continuous state space problems. Meanwhile, state-of-the-art IL algorithms convert behavioral policy learning problems into distribution-matching problems which often require additional online interaction data to be effective. In this paper, we consider the problem of imitation learning in continuous state space environments based solely on observed behavior, without access to transition dynamics information, reward structure, or, most importantly, any additional interactions with the environment. Our approach is based on the Markov balance equation and introduces a novel conditional kernel density estimation-based imitation learning framework. It involves estimating the environment's transition dynamics using conditional kernel density estimators and seeks to satisfy the probabilistic balance equations for the environment. We establish that our estimators satisfy basic asymptotic consistency requirements. Through a series of numerical experiments on continuous state benchmark environments, we show consistently superior empirical performance over many state-of-the-art IL algorithms.

cs.LG↗

arXiv2023

Equivalent and Compact Representations of Neural Network Controllers With Decision Trees

Over the past decade, neural network (NN)-based controllers have demonstrated remarkable efficacy in a variety of decision-making tasks. However, their black-box nature and the risk of unexpected behaviors pose a challenge to their deployment in real-world systems requiring strong guarantees of correctness and safety. We address these limitations by investigating the transformation of NN-based controllers into equivalent soft decision tree (SDT)-based controllers and its impact on verifiability. In contrast to existing work, we focus on discrete-output NN controllers including rectified linear unit (ReLU) activation functions as well as argmax operations. We then devise an exact yet efficient transformation algorithm which automatically prunes redundant branches. We first demonstrate the practical efficacy of the transformation algorithm applied to an autonomous driving NN controller within OpenAI Gym's CarRacing environment. Subsequently, we evaluate our approach using two benchmarks from the OpenAI Gym environment. Our results indicate that the SDT transformation can benefit formal verification, showing runtime improvements of up to $21 \times$ and $2 \times$ for MountainCar-v0 and CartPole-v1, respectively.

cs.LG↗

arXiv2022

Controlling a Markov Decision Process with an Abrupt Change in the Transition Kernel

We consider the control of a Markov decision process (MDP) that undergoes an abrupt change in its transition kernel (mode). We formulate the problem of minimizing regret under control-switching based on mode change detection, compared to a mode-observing controller, as an optimal stopping problem. Using a sequence of approximations, we reduce it to a quickest change detection (QCD) problem with Markovian data, for which we characterize a state-dependent threshold-type optimal change detection policy. Numerical experiments illustrate various properties of our control-switching policy.

eess.SY↗

arXiv2022

Conditional Value at Risk-Sensitive Solar Hosting Capacity Analysis in Distribution Networks

Solar hosting capacity analysis (HCA) assesses the ability of a distribution network to host distributed solar generation without seriously violating distribution network constraints. In this paper, we consider risk-sensitive HCA that limits the risk of network constraint violations with a collection of scenarios of solar irradiance and nodal power demands, where risk is modeled via the conditional value at risk (CVaR) measure. First, we consider the question of maximizing aggregate installed solar capacities, subject to risk constraints and solve it as a second-order cone program (SOCP) with a standard conic relaxation of the feasible set with power flow equations. Second, we design an incremental algorithm to decide whether a configuration of solar installations has acceptable risk of constraint violations, modeled via CVaR. The algorithm circumvents explicit risk computation by incrementally constructing inner and outer polyhedral approximations of the set of acceptable solar installation configurations from prior such tests conducted. Our numerical examples study the impact of risk parameters, the number of scenarios and the scalability of our framework.

eess.SY↗

arXiv2021

Scheduling Flexible Non-Preemptive Loads in Smart-Grid Networks

A market consisting of a generator with thermal and renewable generation capability, a set of non-preemptive loads (i.e., loads which cannot be interrupted once started), and an independent system operator (ISO) is considered. Loads are characterized by durations, power demand rates and utility for receiving service, as well as disutility functions giving preferences for time slots in which service is preferred. Given this information, along with the generator's thermal generation cost function and forecast renewable generation, the social planner solves a mixed integer program to determine a load activation schedule which maximizes social welfare. Assuming price taking behavior, we develop a competitive equilibrium concept based on a relaxed version of the social planner's problem which includes prices for consumption and incentives for flexibility, and allows for probabilistic allocation of power to loads. Considering each load as representative of a population of identical loads with scaled characteristics, we demonstrate that the relaxed social planner's problem gives an exact solution to the original mixed integer problem in the large population limit, and give a market mechanism for implementing the competitive equilibrium. Finally, we evaluate via case study the benefit of incorporating load flexibility information into power consumption and generation scheduling in terms of proportion of loads served and overall social welfare.

eess.SY↗

arXiv2021

Designing Interpretable Approximations to Deep Reinforcement Learning

In an ever expanding set of research and application areas, deep neural networks (DNNs) set the bar for algorithm performance. However, depending upon additional constraints such as processing power and execution time limits, or requirements such as verifiable safety guarantees, it may not be feasible to actually use such high-performing DNNs in practice. Many techniques have been developed in recent years to compress or distill complex DNNs into smaller, faster or more understandable models and controllers. This work seeks to identify reduced models that not only preserve a desired performance level, but also, for example, succinctly explain the latent knowledge represented by a DNN. We illustrate the effectiveness of the proposed approach on the evaluation of decision tree variants and kernel machines in the context of benchmark reinforcement learning tasks.

cs.LG↗

arXiv2021

Two-Stage Electricity Markets with Renewable Energy Integration: Market Mechanisms and Equilibrium Analysis

We consider a two-stage market mechanism for trading electricity including renewable generation as an alternative to the widely used multi-settlement market structure. The two-stage market structure allows for recourse decisions by the market operator, which are not possible in today's markets. We allow for different conventional generation cost curves in the forward and the real-time stages. We have considered costs of demand response programs and black outs, and adopt a DC power flow model to account for network constraints. Our first result is to show existence (by construction) of a sequential competitive equilibrium (SCEq) in such a two-stage market. We argue social welfare properties of such an SCEq, and then design a market mechanism that achieves social welfare maximization when the market participants are non-strategic. We also show that under either a congestion-free or a monopoly-free condition, an efficient Nash equilibrium exists.

cs.GT↗

arXiv2020

A Risk Aware Two-Stage Market Mechanism for Electricity with Renewable Generation

Over the last few decades, electricity markets around the world have adopted multi-settlement structures, allowing for balancing of supply and demand as more accurate forecast information becomes available. Given increasing uncertainty due to adoption of renewables, more recent market design work has focused on optimization of expectation of some quantity, e.g. social welfare. However, social planners and policy makers are often risk averse, so that such risk neutral formulations do not adequately reflect prevailing attitudes towards risk, nor explain the decisions that follow. Hence we incorporate the commonly used risk measure conditional value at risk (CVaR) into the central planning objective, and study how a two-stage market operates when the individual generators are risk neutral. Our primary result is to show existence (by construction) of a sequential competitive equilibrium (SCEq) in this risk-aware two-stage market. Given equilibrium prices, we design a market mechanism which achieves social cost minimization assuming that agents are non strategic.

eess.SY↗

arXiv2018

A Two Stage Mechanism For Selling Random Power

We present a two stage auction mechanism that renewable generators (or aggregators) could use to allocate renewable energy among LSEs. The auction is conducted day- ahead. LSEs submit bids specifying their valuation per unit, as well as their real-time fulfillment costs in case of shortfall in generation. We present an allocation rule and a de-allocation rule that maximizes expected social welfare. Since the LSEs are strategic and may not report their private valuations and costs truthfully, we design a two-part payment, one made in Stage 1, before renewable energy generation level W is realized, and another determined later to be paid as compensation to those LSEs that have to be de-allocated in case of a shortfall. We proposes a two-stage Stochastic VCG mechanism which we prove is incentive compatible in expectation (expected payoff maximizing bidders will bid truthfully), individually rational in expectation (expected payoff of all participants is non-negative) and is also efficient. To the best of our knowledge, this is the first such two-stage mechanism for selling random goods.

cs.GT↗