The sensitivity of forecast-informed reservoir operating policies to forecast attributes (lead-time and skill) in many-objective water systems has been well-established. However, the viability of forecast-informed operations as a climate change adaptation strategy remains underexplored, especially in many-objective systems with complex trade-offs across interests. Little is known about the relationships between forecast attribute and policy robustness under deep uncertainty in future conditions and the relationships between forecast-informed performance and future hydrologic state. This study explores the sensitivity of forecast-informed policy robustness to forecast lead-time and skill in the outflow management plan of the Lake Ontario basin. We create water supply forecasts at four different subseasonal-to-annual lead-times and two levels of skill and further employ a many-objective evolutionary algorithm to discover policies tailored for each forecast case, historical supply conditions, and six objectives. We also leverage a partnership with decision-makers to identify a subset of candidate policies, which are reevaluated under a large set of plausible hydrologic conditions that reflect stationary and nonstationary climates. Scenario discovery techniques are used to map attributes of future hydrology to forecast-informed policy performance. Results show policy robustness is directly related to forecast lead-time, where policies conditioned on 12-month forecasts were more robust under future hydrology. Policies tailored for noisier long-lead forecasts were more robust under a wide range of plausible futures compared with policies trained to perfect forecasts, which highlights the potential to overfit control policies to historical information, even for a forecast-informed policy with perfect foresight. The relationship between performance and the hydrologic regime is dependent on the complexity of the interactions between control decisions and objectives. A threshold of objective performance as a function of supply conditions can support adaptive management of the system. However, more complex interactions make it difficult to identify simple hydrologic indicators that can serve as triggers for dynamic management.
more »
« less
On the Forecast Combination Puzzle
It is often reported in the forecast combination literature that a simple average of candidate forecasts is more robust than sophisticated combining methods. This phenomenon is usually referred to as the “forecast combination puzzle”. Motivated by this puzzle, we explore its possible explanations, including high variance in estimating the target optimal weights (estimation error), invalid weighting formulas, and model/candidate screening before combination. We show that the existing understanding of the puzzle should be complemented by the distinction of different forecast combination scenarios known as combining for adaptation and combining for improvement. Applying combining methods without considering the underlying scenario can itself cause the puzzle. Based on our new understandings, both simulations and real data evaluations are conducted to illustrate the causes of the puzzle. We further propose a multi-level AFTER strategy that can integrate the strengths of different combining methods and adapt intelligently to the underlying scenario. In particular, by treating the simple average as a candidate forecast, the proposed strategy is shown to reduce the heavy cost of estimation error and, to a large extent, mitigate the puzzle.
more »
« less
- Award ID(s):
- 1916376
- PAR ID:
- 10157608
- Date Published:
- Journal Name:
- Econometrics
- Volume:
- 7
- Issue:
- 3
- ISSN:
- 2225-1146
- Page Range / eLocation ID:
- 39
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
In this paper, we study a sampling and transmission scheduling problem for multi-source remote estimation, where a scheduler determines when to take samples from multiple continuous-time Gauss-Markov processes and send the samples over multiple channels to remote estimators. The sample transmission times are i.i.d. across samples and channels. The objective of the scheduler is to minimize the weighted sum of the time-average expected estimation errors of these Gauss-Markov sources. This problem is a continuous-time Restless Multi-armed Bandit (RMAB) problem with a continuous state space. We prove that the bandits are indexable and derive an exact expression of the Whittle index. To the extent of our knowledge, this is the first Whittle index policy for multi-source signal-aware remote estimation of Gauss-Markov processes. We further investigate signal-agnostic remote estimation and develop a Whittle index policy for multi-source Age of Information (AoI) minimization over parallel channels with i.i.d. random transmission times. Our results unite two theoretical frameworks for remote estimation and AoI minimization: threshold-based sampling and Whittle index-based scheduling. In the single-source, single-channel scenario, we demonstrate that the optimal solution to the sampling and scheduling problem can be equivalently expressed as both a threshold-based sampling strategy and a Whittle index-based scheduling policy. Notably, the Whittle index is equal to zero if and only if two conditions are satisfied: (i) the channel is idle, and (ii) the estimation error is precisely equal to the threshold in the threshold-based sampling strategy. Moreover, the methodology employed to derive threshold-based sampling strategies in the single-source, single-channel scenario plays a crucial role in establishing indexability and evaluating the Whittle index in the more intricate multi-source, multi-channel scenario. Our numerical results show that the proposed policy achieves high performance gain over the existing policies when some of the Gauss-Markov processes are highly unstable.more » « less
-
What is the number of rolls of fair 6-sided dice until the first time the total sum of all rolls is a prime? We compute the expectation and the variance of this random variable up to an additive error of less than 10−⁴. This is a solution to a puzzle suggested by DasGupta (2017) in the Bulletin of the Institute of Mathematical Statistics, where the published solution is incomplete. The proof is simple, combining a basic dynamic programming algorithm with a quick Matlab computation and basic facts about the distribution of primes.more » « less
-
This paper presents methods for placing length sensors on a soft continuum robot joint as well as a novel configuration estimation method that drastically minimizes configuration estimation error. The methods utilized for placing sensors along the length of the joint include a single joint length sensor, sensors lined end-to-end, sensors that overlap according to a heuristic, and sensors that are placed by an optimization that we describe in this paper. The methods of configuration estimation include directly relating sensor length to a segment of the joint's angle, using an equal weighting of overlapping sensors that cover a joint segment, and using a weighted linear combination of all sensors on the continuum joint. The weights for the linear combination method are determined using robust linear regression. Using a kinematic simulation we show that placing three or more overlapping sensors and estimating the configuration with a linear combination of sensors resulted in a median error of 0.026% of the max range of motion or less. This is over a 500 times improvement as compared to using a single sensor to estimate the joint configuration. This error was computed across 80 simulated robots of different lengths and ranges of motion. We also found that the fully optimized sensor placement performed only marginally better than the placement of sensors according to the heuristic. This suggests that the use of a linear combination of sensors, with weights found using linear regression is more important than the placement of the overlapping sensors. Further, using the heuristic significantly simplifies the application of these techniques when designing for hardware.more » « less
-
We investigate a scenario where a chaser spacecraft or satellite equipped with a monocular camera navigates in close proximity to a target spacecraft. The satellite’s primary objective is to construct a representation of the operational environment and localize itself within it, utilizing the available sensor data. We frame the joint task of state trajectory and map estimation as an instance of smoothing-based simultaneous localization and mapping (SLAM), where the underlying structure of the problem is represented as a factor graph. Rather than considering estimation and planning as separate tasks, we propose to control the camera observations to actively reduce the uncertainty of the estimation variables, the spacecraft state, and the map landmarks. This is accomplished by adopting an information-theoretic metric to reason about the impact of candidate actions on the evolution of the belief state. Numerical simulations indicate that our proposed method successfully captures the interplay between planning and estimation, hence yielding reduced uncertainty and higher accuracy when compared to commonly adopted passive sensing strategies.more » « less
An official website of the United States government

