Regret Minimization Research Articles

Accommodating exogenous variable and decision rule heterogeneity in discrete choice models: Application to bicyclist route choice.

The proposed research contributes to our understanding of incorporating heterogeneity in discrete choice models with respect to exogenous variables and decision rules. Specifically, the proposed latent segmentation based mixed models segment population to different classes with their own decision rules while also incorporating unobserved heterogeneity within the segment level models. In our analysis, we choose to consider both random utility and random regret theories. Further, instead of assuming the number of segments (as 2), we conduct an exhaustive exploration with multiple segments across the two decision rules. The model estimation is conducted using a stated preference data from 695 commuter cyclists compiled through a web-based survey. The probabilistic allocation of respondents to different segments indicates that female commuter cyclists are more utility oriented; however, the majority of the commuter cyclist’s choice pattern is consistent with regret minimization mechanism. Overall, cyclists’ route choice decisions are influenced by roadway attributes, cycling infrastructure availability, pollution exposure, and travel time. The analysis approach also allows us to investigate time based trade-offs across cyclists belonging to different classes. Interestingly, we observe that the trade-off values in regret and utility based segments for roadway attributes are similar in magnitude; but the values differ greatly for cycling infrastructure and pollution exposure attributes, particularly for maximum exposure levels.

Travel Choice Analysis under Metro Emergency Context: Utility? Regret? Or Both?

With the continuous expansion of the network scale and increasing of passengers, metro emergencies such as operational equipment failure are happening more frequently. Due to the narrow space and crowds of people, metro emergencies always have more of an impact than road traffic emergencies. In order to adopt appropriate measures to ensure passenger safety and avoid risks, we need to get a better understanding of passengers’ travel choice behaviors under emergencies. Most of the existing research studies related to travel choice behaviors took the random utility maximization (RUM) principle for granted, but failed to realize the potential of different decision-making processes and changes to the decision-making environment. In this research, we aim to analyze metro passengers’ travel choice behaviors under metro network emergency contexts. Based on the data collected from a survey about travel choices under metro emergencies in the Guangzhou Metro, we compared the performances of models that follow the RUM and random regret minimization (RRM) principles, and established a hybrid RUM-RRM model as well as a nested logit model following RRM (NL-RRM) to estimate the effects of various factors on passengers’ travel choice behaviors. Comparisons illustrate that the hybrid model and NL-RRM model can improve model fit, and the combination of RUM and RRM outperforms either of them respectively.

Tolerance and Indifference Bands in Regret–Rejoice Choice Models: Extension to Market Segmentation in the Context of Mode Choice Behavior

Random regret minimization models (RRMs), based on seminal work in regret theory, have been introduced into transportation research as an alternative to expected/random utility models. With ample applications in diverse choice contexts, the RRMs have been extended to include the effect of “rejoice,” the counterpart of the emotion of regret. The fundamental assumption of regret–rejoice models is that when the chosen alternative is inferior to non-chosen alternatives with respect to an attribute, individuals feel regret; otherwise, if the chosen alternative is superior to non-chosen alternatives, individuals rejoice. The regret and rejoice functions are assumed to be continuous in attribute differences. However, individuals may tolerate small attribute differences when judging regret and be indifferent to small differences when assessing rejoice. This paper therefore introduces tolerance and indifference bands in random regret–rejoice choice models, and compares the performance of these models against the performance of the original models. Furthermore, it is assumed that tolerance and indifference bands differ by trip purpose. Empirical results testify to the better performance of the models with the tolerance and indifference bands, and show that trip purpose is an important factor affecting tolerance and indifference bands.

Faster algorithms for extensive-form game solving via improved smoothing functions

Sparse iterative methods, in particular first-order methods, are known to be among the most effective in solving large-scale two-player zero-sum extensive-form games. The convergence rates of these methods depend heavily on the properties of the distance-generating function that they are based on. We investigate both the theoretical and practical performance improvement of first-order methods (FOMs) for solving extensive-form games through better design of the dilated entropy function—a class of distance-generating functions related to the domains associated with the extensive-form games. By introducing a new weighting scheme for the dilated entropy function, we develop the first distance-generating function for the strategy spaces of sequential games that has only a logarithmic dependence on the branching factor of the player. This result improves the overall convergence rate of several FOMs working with dilated entropy function by a factor of $$\Omega (b^dd)$$, where b is the branching factor of the player, and d is the depth of the game tree. Thus far, counterfactual regret minimization methods have been faster in practice, and more popular, than FOMs despite their theoretically inferior convergence rates. Using our new weighting scheme and a practical parameter tuning procedure we show that, for the first time, the excessive gap technique, a classical FOM, can be made faster than the counterfactual regret minimization algorithm in practice for large games, and that the aggressive stepsize scheme of CFR+ is the only reason that the algorithm is faster in practice.

Two MAGDM models based on hesitant fuzzy linguistic term sets with possibility distributions: VIKOR and TOPSIS

Hesitant fuzzy linguistic term sets (HFLTSs) with additional possibility distributions can represent a much broader range of linguistic data. This paper develops compromise solutions for multiple attribute group decision making (MAGDM) using HFLTS. Geodesic distance and possibility distribution based distance measures are introduced to calculate the consensus degrees and determine the participant importance weights for the aggregation. Two models are then proposed to derive a compromise solution for the MAGDM problems. The first model is based on the VIKOR method and is used to determine the compromise between group utility maximization and individual regret minimization. The second model is based on the TOPSIS method and seeks to identify the compromise between the distances from the ideal and anti-ideal solutions. For both models, several ideal solutions and separation measures are presented and some of the properties in the two models are proven. An example based on an assessment of a health-care waste disposal management system illustrates the feasibility and practicability of the two proposed models. A further comparative study highlights the distinct features and potential use of the presented models.

A regret-based route choice model with asymmetric preference in a stochastic network

In this study, a stochastic user equilibrium model on the modified random regret minimization is proposed by incorporating the asymmetric preference for gains and losses to describe its effects on the regret degree of travelers. Travelers are considered to be capable of perceiving the gains and losses of attributes separately when comparing between the alternatives. Compared to the stochastic user equilibrium model on the random regret minimization model, the potential difference of emotion experienced induced by the loss and gain in the equal size is jointly caused by the taste parameter and loss aversion of travelers in the proposed model. And travelers always tend to use the routes with the minimum perceived regret in the travel decision processes. In addition, the variational inequality problem of the stochastic user equilibrium model on the modified random regret minimization model is given, and the characteristics of its solution are discussed. A route-based solution algorithm is used to resolve the problem. Numerical results given by a three-route network show that the loss aversion produces a great impact on travelers’ choice decisions and the model can more flexibly capture the choice behavior than the existing models.

Hypothetical bias and decision-rule effect in modelling discrete directional choices

IntroductionThis empirical study investigates, in parallel, two key questions in relation with modelling discrete choices. (i) To what extent econometric modelling estimates and predictions derived from responses to hypothetical choice scenarios differ from those of an equivalent realistic choice context (i.e. hypothetical bias)? (ii) To what extent econometric modelling estimates and predictions differ as a result of postulating “regret minimisation” as the decision rule as opposed to the “utility maximisation” assumption (i.e. decision-rule effect)? The magnitude of these two effects are also compared relatively. MethodsWe explore the two aforementioned problems in the context of discrete directional choices. Disaggregate experimental observations are collected from both stated-choice (SC) and realistic (or experimentally revealed) choice (RC) settings. We perform our analyses on the basis of four distinct criteria: parameter estimates, parameter ratios, predictions and prediction errors (in terms of disaggregate (i.e. individual-level) choice probabilities)). Results(i) Our results displayed a great degree of resemblance between the parameter estimate patterns emerged from both data sources including a perfect match between the sign and significance of the SC and RC estimates. Major observed discrepancies, however, were related to the scale of the estimates as well as certain coefficient ratios. In terms of the predictions (i.e. simulated probabilities) and prediction errors (i.e. based on a hold-out part of the sample), SC-based models performed surprisingly similar to those of their RC-based counterparts. (ii) The assumption of the decision rule made even a much less noticeable modelling difference (compared to the hypothetical bias) in both parameter estimates and predictions. The shift from utility to regret model led to only marginal differences in estimates, simulated probabilities and prediction errors. Compared to the hypothetical bias in particular, decision-rule specification was a much less impactful modelling component. ApplicationsThese findings contribute to the accumulation of the empirical evidence that can determine how and when one can make best use of the SC methods which, in essence, demands the creation of links between hypothetical and real data in various contexts of choice. Our results suggested that, at least in certain contexts and applications, choice elicitation outcomes are reasonably consistent between the hypothetical and realistic settings. The findings also add to the existing evidence that point at the virtual neutrality of the discrete-choice modelling outcomes to the use of utility versus regret optimisation assumption as the choice rule. Future directionsThe study also leaves us with the further question of how the observed similarity/dissimilarity patterns (SC versus RC; and regret versus utility) would materialise if aggregate prediction measures are of main concern (as opposed to the use of disaggregate measures). The question has particular bearings on applications in which discrete-choice models are applied to simulate or predict a whole system (i.e. when discrete choice models perform as part of a broader model) as a common practice in transport studies. This question will be investigated in a subsequent work.

Toward a Quality-Aware Online Pricing Mechanism for Crowdsensed Wireless Fingerprints

Fingerprinting localization systems are outstanding for its convenient deployment, where a major challenge is the high cost for collecting a huge number of received signal strength fingerprints. Mobile crowdsensing (MCS) paradigm is cost-effective for large-scale data collection; however, a quality-aware data pricing mechanism dedicated to MCSed fingerprints accommodating practical application situations including budget constraints and online data submission is still unavailable. In this paper, we present a data pricing scheme dedicated to MCSed fingerprints by enhancing the online learning technique. We first reveal the principle of fingerprints quality assessment for accurate localization. Based on the principle, we design corresponding loss and regret function, which is able to reflect values of the fingerprints with respect to localization accuracy. We then present an online pricing scheme for MCSed data, which results in that the worker's payoff is a random variable following an optimal probability density function leading to the minimum expected regret. Furthermore, we extend our scheme to application scenarios with different budget settings, where the pricing strategies for the scenarios of regret minimization with fixed budget and budget minimization for certain fingerprints quality level are investigated. Experimental results are presented to verify our theoretical analysis.

Freight Mode Choice: A Regret Minimization and Utility Maximization Based Hybrid Model

With the introduction of automated vehicles, the performance of the trucking industry is expected to be improved. In fact, this may impact the entire freight transportation system as trucks possess the highest mode share in freight transportation. To investigate this impact, a hybrid utility–regret-based mode choice model accommodating for shipper level unobserved heterogeneity is proposed in this study. It recognizes that not all attributes influencing shipment mode are evaluated following a homogenous decision rule (solely random utility maximization/solely random regret minimization). The proposed model system is developed using 2012 Commodity Flow Survey data. To demonstrate the applicability of the proposed model system, a detailed policy analysis is conducted considering several futuristic scenarios such as implementation of automation and controlled access of truck traffic to an urban region. The results indicate that introduction of automation in the freight industry would be more beneficial for long-haul hire truck mode than short-haul private truck mode. An increase in truck shipping time due to re-routing of truck traffic away from urban regions causes a modal shift from truck to parcel and “other” mode (rail, water or multiple modes).

Designing coalition-based fair and stable pricing mechanisms under private information on consumers’ reservation prices

We model the relation between an aggregator and consumers joining a coalition to reduce the risk resulting from the unpredictability of their base load demand, as a Stackelberg game formulated as a mathematical bilevel program with private information on the consumers’ reservation prices. At the upper-level of the Stackelberg game, the aggregator optimizes his daily price profile so as to reach a net targeted profit which is the maximum value guaranteeing that no consumer will leave the coalition - to contract with a conventional retailer considered here as a fixed alternative - while meeting fairness criterion imposed by the cost-sharing mechanism. At the lower-level, the consumers are asked to provide in day ahead an estimate of their base load hourly demand profile and to schedule their shiftable loads depending on the price signal sent by the aggregator. We provide algorithms that determine the unique price profile and consumer shiftable load schedules as functions of the reservation price estimates. The Stackelberg game between the aggregator and the consumers being repeated for a period of time, the aggregator has the possibility to update his estimates of the reservation prices relying on a feedback function which depends on the percentage of activated loads. A randomized algorithm for consumers’ reservation price learning based on regret minimization is provided. For four cost-sharing mechanisms such as uniform allocation, stand-alone cost, Shapley value, separable and non-separable costs, we determine the closed form of the aggregator’s optimal net targeted profit guaranteeing the stability of the coalition. We also determine conditions guaranteeing the core non-emptiness and prove that for a profit-maximizing aggregator, the stand-alone cost is always preferable to the Shapley value, which coincides with the uniform allocation. Furthermore, the optimal size of the coalition - in terms of the aggregator’s profit - can be determined analytically when the Shapley value is implemented as cost-sharing mechanism. The results are illustrated on a case study where we show that there exists an optimal net targeted profit below which the consumers energy bill is lower when joining the aggregator than with the conventional retailer. Coalition dynamics is also analyzed numerically depending on the consumer inertia in their energy supplier choice process, for each cost-sharing mechanism.

Investigating Behavioral Differences in Heterogeneous Decision Rule Segments: An Empirical Analysis

Conventional and contemporary models of travel choice make the restrictive assumption of homogeneity in decision rules. Recent literature has shown empirical evidence for potential heterogeneity in decision rules with regard to utility maximization and regret minimization. Notwithstanding these advances in modeling decision rules, behavioral understanding in the differences in these alternative decision rule segments has not been sufficiently understood. Moreover, the factors which influence the choice of these decision rules have not received significant attention. This study proposes a framework which considers decision makers to have both utility maximizing and regret minimizing tendencies. The variation in these tendencies across decision makers renders the framework heterogeneous. A heterogeneous decision rule model is developed assuming the decision rule adopted to be a latent construct. The study characterizes the regret minimizing and utility maximizing segments based on average values of the segmental attributes. The empirical findings show evidence to confirm that utility maximizers tend to be predominantly captive to personal vehicle usage while regret minimizers might be non-captive to any particular mode. The nature and extent of influence of factors affecting the choice of decision rule is also examined.

Regret Minimization for Primary/Secondary Access to Satellite Resources With Cognitive Interference

There are different forms of uncertainty in satellite communications, including cognitive interferers, channel conditions, packet traffic, and spectrum occupancy of users across channels. In addition, delay (such as propagation delay observed over satellite links) increases spectrum uncertainty and makes spectrum sensing and spectrum access two challenging tasks. To address such challenges, this paper presents a regret minimization solution for primary user (PU) and secondary user (SU) spectrum access to satellite resources in the presence of cognitive interferers. This robust game theoretic solution supports hierarchical spectrum sharing and dynamic spectrum access over multiple channels. Users select channels for data transmission and perform power control to optimize individual utility functions that are random due to different forms of uncertainty. The proposed game engine based on regret minimization framework provides a low-complexity and fast solution compared with traditional game solutions based on expected utility maximization. Detailed numerical results evaluate throughput and delay of PUs and SUs in the presence of cognitive interferers and compare the robust game theory-enabled approach with two benchmark schemes (with and without knowledge on channel availability). To support controllable and repeatable test and evaluation with real radios, an emulation testbed is built with software-defined radios connected with a network channel emulator that generates channel, mobility, and interference effects for satellite communications. GNU Radio modules are developed for cognitive network functionalities and run on USRP N210 radios that represent SU, PU, interferer, and satellite nodes. Emulation tests validate the effectiveness of the proposed solution under real radio effects.

Travel Mode and Travel Route Choice Behavior Based on Random Regret Minimization: A Systematic Review

In recent years, traffic congestion has become increasingly serious and the urban environment has deteriorated, posing a challenge to the modern sustainable transportation system. Sustainable travel behavior is a solution that many scholars recognize as being an important aspect in the development of socially, environmentally, and economically sustainable communities. Increasing numbers of studies analyzed the travel choice behavior based on Random Regret-Minimization (RRM) model. RRM considers multiple attribute compromises to capture the traveler’s choice behavior based on minimizing the perceived regret decision criteria. Travel route choice and travel mode choice are interrelated and mutual restraint when a traveler makes a travel decision. To our knowledge, there are limited literatures that overall considered travel mode and travel route choice behavior based on RRM at present. This paper aims to fill this gap and presents a literature review for the application of RRM on sustainable travel mode and travel route choice behavior from empirical issues, influencing factors, theories and methods to evaluate RRM’s potential and limitations as a discrete model of travel choice behavior. The results will provide reference for researchers to study this field and develop novel strategies to promote the sustainable traffic system in the future.

Primal–Dual Algorithms for Convex Optimization via Regret Minimization

We consider a large-scale convex program with functional constraints, where interior point methods are intractable due to the problem size. The effective solution techniques for these problems permit only simple operations at each iteration, and thus are based on primal–dual first-order methods such as the Arrow–Hurwicz–Uzawa subgradient method, which utilize only gradient computations and projections at each iteration. Such primal–dual algorithms admit the interpretation of solving the associated saddle point problem arising from the Lagrange dual. We revisit these methods through the lens of regret minimization from online learning and present a flexible framework. While it is well known that two regret-minimizing algorithms can be used to solve a convex–concave saddle point problem at the standard rate of $O$ ( $1/\sqrt {T}$ ), our framework for primal–dual algorithms allows us to exploit structural properties such as smoothness and/or strong convexity and achieve better convergence rates in favorable cases. In particular, for non-smooth problems with strongly convex objectives, our primal–dual framework equipped with an appropriate modification of Nesterov’s dual averaging algorithm achieves $O$ ( $1/T$ ) convergence rate.

A comparison of regret-based and utility-based discrete choice modelling – an empirical illustration with hospital bed choice

ABSTRACTThere is some concern that the unobserved preference heterogeneity in random utility maximization theory-based discrete choice experiment modelling is an important source of error variability. The randomness in utility is often interpreted as interpersonal preference heterogeneity but it can also be intrapersonal random variation in preferences. We compare utility maximization and regret minimization-based choice models’ sensitivity to individual heterogeneity, examine differences between two consecrated models and validate with empirical illustrations. We use frequency of category (public, semi-private, and private) of bed chosen from Swiss cross-sectional datasets (2007–2012) to compare two approaches – utility maximization and regret minimization by applying multinomial logit (MNL) models in regard to the variances in utility (regret) function, goodness-of-fit and predicted marginal effects (pseudo-elasticity) of additional payment. We find parameters with the same sign and estimates with almost same order of magnitude in both the approaches. The statistical significance of attribute effects is consistent in all variants of utility -based MNL models while effects of different attributes are significant only in heteroskedastic extreme value (HEV) variant of regret-based MNL models. This empirical illustration suggests that HEV variant of regret-based models perform better in capturing attribute effects in choice behaviour.

Application of rrm as behavior mode choice on modelling transportation

Transportation mode selection, the first step in transportation planning process, is probably one of the most important planning elements. The development of models that can explain the preference of passengers regarding their chosen mode of public transport option will contribute to the improvement and development of existing public transport. Logit models have been widely used to determine the mode choice models in which the alternative are different transport modes. Random Regret Minimization (RRM) theory is a theory developed from the behavior to choose (choice behavior) in a state of uncertainty. During its development, the theory was used in various disciplines, such as marketing, micro economy, psychology, management, and transportation. This article aims to show the use of RRM in various modes of selection, from the results of various studies that have been conducted both in north sumatera and western Java.

Does the decision rule matter for large-scale transport models?

This paper is the first to study to what extent decision rules, embedded in disaggregate discrete choice models, matter for large-scale aggregate level mobility forecasts. Such large-scale forecasts are a crucial underpinning for many transport infrastructure investment decisions. We show, in the particular context of (linear-additive) utility maximization (RUM) and regret minimization (RRM) rules, that the decision rule matters for aggregate level mobility forecasts. We find non-trivial differences between the RUM-based and RRM-based transport model in terms of aggregate forecasts of passenger kilometers, demand elasticities, and monetary benefits of transport policies. This opens up new opportunities for policy analysts to enrich their sensitivity analysis toolbox.

Selection of automatic short answer grading techniques using contextual bandits for different evaluation measures

Automatic short answer grading (ASAG) systems are designed to automatically assess short answers in natural language having a length of a few words to a few sentences. Many ASAG techniques have been proposed in the literature. In this paper, we critically analyse the role of evaluation measures used for assessing the quality of ASAG techniques. In real-world settings, multiple factors such as, difficulty level, and diversity of student answers, vary significantly across questions, leading to different ASAG techniques emerging as superior for different evaluation measures. Building upon this observation, we propose to automatic learning of a mapping from questions to ASAG techniques using minimal human (expert/crowd) feedback. We do this by formulating the learning task as a contextual bandits problem and providing a rigorous regret minimization algorithm that handles key practical considerations, such as, noisy experts and similarity between questions. Our approach offers the flexibility to include new ASAG systems on the fly and does not require the human expert to have knowledge of the working details of the system while providing feedback. With extensive simulations on a standard dataset, we demonstrate that our approach yields outcomes that are remarkably consistent with human evaluations.

The effect of attribute-alternative matrix displays on preferences and processing strategies

When analyzing discrete choice data we assume that respondents compare alternatives and make a utility maximizing choice. The majority of DCEs use a matrix display with one row per attribute and one column per alternative. A comparison by alternatives implies that respondents process the choice task column-by-column. However, evidence from psychology and judgment and decision making research suggest that learned reading patterns dominate and as such the standard matrix display might induce processing by attributes rather than alternatives. We test this using a split sample survey conducted in France where respondents were randomly allocated into a standard or transposed matrix display group. Our results show that there is no difference in relative scale between the two groups, but that elicited preferences differ. Importantly, ASCs are insignificant in the transposed condition. We find no difference in propensity to use simplifying strategies, but respondents in the standard display condition are more likely to choose according to a random regret minimization (RRM) model rather than random utility model (RUM). We discuss the implications of our findings for future discrete choice experiments.

On the robustness of efficient experimental designs towards the underlying decision rule

We present a methodology to derive efficient designs for Stated Choice (SC) experiments based on Random Regret Minimisation (RRM) behavioural assumptions. This complements earlier work on the design of efficient SC experiments based on Random Utility Maximisation (RUM) models. Capitalizing on this methodology, and using both analytical derivations and empirical data, we investigate the importance of the analyst’s assumption regarding the underlying decision rule used to generate the efficient experimental design. We find that conventional RUM-efficient designs can be statistically highly inefficient in cases where RRM is the better representation of the actual choice behaviour, and vice versa. Furthermore, we present a methodology to construct efficient designs that are robust towards the uncertainty on the side of the analyst regarding the underlying decision rule.