A Robust Utility Learning Framework via Inverse Optimization

In many smart infrastructure applications, flexibility in achieving sustainability goals can be gained by engaging end users. However, these users often have heterogeneous preferences that are unknown to the decision maker tasked with improving operational efficiency. Modeling user interaction as a continuous game between noncooperative players, we propose a robust parametric utility learning framework that employs constrained feasible generalized least squares estimation with heteroskedastic inference. To improve forecasting performance, we extend the robust utility learning scheme by employing bootstrapping with bagging, bumping, and gradient boosting ensemble methods. Moreover, we estimate the noise covariance, which provides approximated correlations between players, which we leverage to develop a novel correlated utility learning framework. We apply the proposed methods both to a toy example arising from Bertrand-Nash competition between two firms and to data from a social game experiment designed to encourage energy efficient behavior among smart building occupants. Using occupant voting data for shared resources such as lighting, we simulate the game defined by the estimated utility functions to demonstrate the performance of the proposed methods.

[1]  G. G. Stokes "J." , 1890, The New Yale Book of Quotations.

[2]  J. Goodman Note on Existence and Uniqueness of Equilibrium Points for Concave N-Person Games , 1965 .

[3]  R. Aumann Subjectivity and Correlation in Randomized Strategies , 1974 .

[4]  A. Tversky,et al.  The framing of decisions and the psychology of choice. , 1981, Science.

[5]  M. Gendreau On the location of eigenvalues of off-diagonal constant matrices , 1986 .

[6]  John H. Sheesley,et al.  Quality Engineering in Production Systems , 1988 .

[7]  S. Flåm Solving non-cooperative games by continuous subgradient projection methods , 1990 .

[8]  Robert Tibshirani,et al.  Model Search and Inference By Bootstrap "bumping , 1995 .

[9]  Steven T. Berry,et al.  Automobile Prices in Market Equilibrium , 1995 .

[10]  Clifford M. Hurvich,et al.  Smoothing parameter selection in nonparametric regression using an improved Akaike information criterion , 1998 .

[11]  J. Laitner Energy efficiency: rebounding to a sound analytical perspective , 2000 .

[12]  L. Schipper,et al.  On the rebound? Feedback between energy intensities and energy uses in IEA countries , 2000 .

[13]  J. Friedman Greedy function approximation: A gradient boosting machine. , 2001 .

[14]  Kevin Barraclough,et al.  I and i , 2001, BMJ : British Medical Journal.

[15]  J. Laffont,et al.  The Theory of Incentives: The Principal-Agent Model , 2001 .

[16]  Eric R. Ziegel,et al.  The Elements of Statistical Learning , 2003, Technometrics.

[17]  Francisco Cribari-Neto,et al.  Asymptotic inference under heteroskedasticity of unknown form , 2004, Comput. Stat. Data Anal..

[18]  J. Franklin,et al.  The elements of statistical learning: data mining, inference and prediction , 2005 .

[19]  David A. Freedman,et al.  Statistical Models: Theory and Practice: References , 2005 .

[20]  Magnus Bång,et al.  The PowerHhouse: A Persuasive Computer Game Designed to Raise Awareness of Domestic Energy Consumption , 2006, PERSUASIVE.

[21]  Christoph F. Reinhart,et al.  Adding advanced behavioural models in whole building energy simulation: A study on the total energy impact of manual and automated lighting control , 2006 .

[22]  Rob J Hyndman,et al.  Another look at measures of forecast accuracy , 2006 .

[23]  T. Mulgan The Contract Theory , 2006 .

[24]  M. Boman,et al.  Energy Saving and Added Customer Value in Intelligent Buildings , 2007 .

[25]  David E. Culler,et al.  Design and implementation of a high-fidelity AC metering network , 2009, 2009 International Conference on Information Processing in Sensor Networks.

[26]  Y. Narahari,et al.  Game Theoretic Problems in Network Economics and Mechanism Design Solutions , 2009, Advanced Information and Knowledge Processing.

[27]  Rolf Isermann,et al.  Identification of Dynamic Systems: An Introduction with Applications , 2010 .

[28]  Andrew Ledvina,et al.  Dynamic Bertrand Oligopoly , 2010, 1004.1726.

[29]  Stephen P. Boyd,et al.  Imputing a convex objective function , 2011, 2011 IEEE International Symposium on Intelligent Control.

[30]  David E. Culler,et al.  Identifying models of HVAC systems using semiparametric regression , 2012, 2012 American Control Conference (ACC).

[31]  M. Jahn,et al.  Saving energy at work: the design of a pervasive game for office spaces , 2012, MUM.

[32]  Claire J. Tomlin,et al.  Incentive design for efficient building quality of service , 2012, 2012 50th Annual Allerton Conference on Communication, Control, and Computing (Allerton).

[33]  Henrik Ohlsson,et al.  Incentive Design and Utility Learning via Energy Disaggregation , 2013, 1312.1394.

[34]  Ming Jin,et al.  Social game for building energy efficiency: Incentive design , 2014, 2014 52nd Annual Allerton Conference on Communication, Control, and Computing (Allerton).

[35]  MengChu Zhou,et al.  Social incentive policies to engage commercial building occupants in demand response , 2014, 2014 IEEE International Conference on Automation Science and Engineering (CASE).

[36]  PresenceSense: Zero-training Algorithm for Individual Presence Detection based on Power Monitoring , 2014, 1407.4395.

[37]  Ming Jin,et al.  PresenceSense: zero-training algorithm for individual presence detection based on power monitoring , 2014, BuildSys@SenSys.

[38]  Lillian J. Ratliff,et al.  Incentivizing Efficiency in Societal-Scale Cyber-Physical Systems , 2015 .

[39]  Ming Jin,et al.  Sensing by Proxy : Occupancy Detection Based on Indoor CO 2 Concentration , 2015 .

[40]  Ming Jin,et al.  REST: a reliable estimation of stopping time algorithm for social game experiments , 2015, ICCPS.

[41]  Vishal Gupta,et al.  Data-driven estimation in equilibrium using inverse optimization , 2013, Mathematical Programming.

[42]  S. Shankar Sastry,et al.  On the Characterization of Local Nash Equilibria in Continuous Games , 2014, IEEE Transactions on Automatic Control.

[43]  Ming Jin,et al.  Inverse modeling of non-cooperative agents via mixture of utilities , 2016, 2016 IEEE 55th Conference on Decision and Control (CDC).

[44]  Ming Jin,et al.  Virtual Occupancy Sensing: Using Smart Meters to Indicate Your Presence , 2017, IEEE Transactions on Mobile Computing.

[45]  Ming Jin,et al.  MOD-DR: Microgrid optimal dispatch with demand response , 2017 .

[46]  Kevin Weekly,et al.  Occupancy Detection via Environmental Sensing , 2018, IEEE Transactions on Automation Science and Engineering.

[47]  K. Schittkowski,et al.  NONLINEAR PROGRAMMING , 2022 .