6

First, theremay be irreducible noise in the measurement process itself

In general, when all agents learn simultaneously, the found best response may not beunique (Shoham and Leyton-Brown 2008).

A special case of the MG is the stateless setting X = � called strategic-form game 2 .Strategic-form games describe one-shot interactions where all agents simultaneouslyexecute an action and receive a reward based on the joint action after which the gameends.

Finally, 𝛾 ∈ [0, 1)describes the discount factor.

Moreover, these stepsare not themselves rewarding and they will be separated from each other and any reward bylong periods of time, during which you will engage with other life tasks.

This individualization, if it takes place, triggers its own fairness anddiscrimination issues. First, since it would lead to more disparate pricing, individuals foundas “the riskiest” by the algorithm are likely to get unaffordable premiums, hence excludingthem from the insured community.

or Simon(1988) and Horan (2021), the adoption of this individual point of view by the judge in theNorris case has contributed to reinforcing the erasure of the principle of solidarity whichis at the heart of insurance practice (Lehtonen and Liukko (2011)).

On the other hand, the newtechniques often appear to be the continuation of this almost age-old segmentation practice(Swedloff (2014))

Measuring the impact on insuranceis however maybe more difficult than in other areas. On the one hand, like any otherorganization, insurers are pushed to change their practices to incorporate the new sources ofdata that have become available, the increased computing capacity, and the new algorithms.

Recently, the emergence of big data and new algorithmson insurance actually revived and renewed, with obvious points of continuity and rupture,older debates linked to discrimination in insurance. Conceptually however, these changes areshaking up insurance practice: the ’individualization’ of risks, rendered possible by thesenew technologies, is indeed now considered as fairer than their pooling. Finally, the last partdiscusses the ethical issues of big data for insurance, in comparison with various notions ofalgorithmic fairness.

Since the beginning of their history, insurers have been quantifying human phenomena,collecting and using data to classify and price risks. This practice is not trivial: insuranceplays a major role in industrialized societies in opening or closing life opportunities (Horan(2021) or Baker and Simon (2002)). As such, insurers were confronted early on with theequity issues associated with data. As early as 1909, the Kansas insurance regulator thusdrew the contours of fair rating practice: he defined a rating as "not unfairly discriminatory"if it treats similar people in the same way (Frezal and Barry (2019), Miller (2009)) orBarry and Charpentier (2022).

machine learning

n practice, regional differences in investment costsexist, but since renewable investment costs are empirically shown to be driven down byglobal cumulative installed capacity – in a process of global “learning” or “experience”(Hepburn et al. (2020), Way et al. (2021)) – the global average represents a robust proxy

To calculate investment costs for differenttypes of renewable energy investments needed to replace coal we use data from IRENA(2021b).

ntation details. • Data preparation: All our timeseries data that enter to CALIBNN are padded with a mini-mum sequence length of 20 for COVID and 5 for influenza.We also normalize each features with mean 0 and variance1. To inform CALIBNN of the county to predict, we usea one hot encoding for counties. • Architecture details:In CALIBNN, the encoder is a 2-layer bidirectional GRUand decoder is a 1-layer bidirectional GRU, both with hid-den size of 32. Output layer has two linear layers of size32x16xD with ReLU activation function and D is ABMparameter dimensions dimensions: D = 3 for COVID-19and D = 2 for flu. • Hyperparameters: We found a learningrate of 10−3, Xavier initialization, and the Adam optimiza-tion algorithm work best. • ABM parameters (θP , θT ):For COVID-19, we have three parameters: R0, mortalityrate, and initial infections percentage. These are boundedwith θL = [1.0, 0.001, 0.01] and θU = [8.0, 0.02, 1.0]. Forflu, we have two parameters: R0 and initial infections per-centage. These are bounded with θL = [1.05, 0.1] andθU = [2.6, 5.0]. The initial infections percentage is thepercentage of the population that is infected at time stept = 0 of the simulation. • ABM clinical parameters: Toset some of the parameters of our transmission and progres-sion models, we utilize clinical data from reliable sources.Specifically, for COVID-19 we use age-stratified suscep-tibility and parameters of a scaled gamma distribution torepresent infectiousness as a function of time as per ( 35 ; 31 ).For influenza, we set those parameters based on CDC flufacts (1).Target variables. The target variable for COVID-19 isCOVID-associated mortality, while in flu we use influenza-like-illness (ILI) counts, which is collected by the CDC. ILImeasures the percentage of healthcare seekers who exhibitinfluenza-like-illness symptoms, defined as ”fever (tempera-ture of 100°F/37.8°C or greater) and a cough and/or a sorethroat without a known cause other than influenza” ( 32).The ground truth data for the target variables is obtaineduploads/MMWR_Week_overview.pdf4https://predict.cdc.gov/from JHU CSSE COVID-19 data repository and ILI fromCDC influenza dashboard.Details on baseline implementation. Vanilla-ABM: Asnoted in the main paper, R0 and case-fatality rate are ob-tained from authoritative sources. To set the initial infectionspercentage for this baseline, we set it to the mean value ofthe search range. PC-ABM: We present details on each ofthe ODE models we used for this baseline.(COVID-19) SEIRM (63): The SEIRM model consists offive compartments: Susceptible (S), Exposed (E), Infected(I), Recovered (R), and Mortality (M ). It is parameterizedby four variables Ω = {β, α, γ, μ}, where β is the infectiv-ity rate, 1/α is the mean latent period for the disease, 1/γ isthe mean infectious period, and μ is the mortality rate. Thebasic reproductive number R0 = β/(γ + μ).dStdt = −βtStItNdEdt = βtStItN − αtEt (9)dItdt = αtEt − γtIt − μtItdRtdt = γtItdMtdt = μtIt(Flu) SIRS (58): This model consists of three compartments:Susceptible (St), Infected (It), and Recovered (Rt). It isparameterized by three variables Ω = {β, D, L}, where βis the infectivity rate, D is the mean duration of immunity,and L is the mean duration of the immunity period. Thebasic reproductive number R0 = βD.dStdt = N − St − ItLt− βtItStN (10)dItdt = βtItStN − ItDtD. More details on evaluating policyinterventionsWe reproduce the experimental setup in ( 53). For inter-ventions, we simulate standard covid-19 vaccination ver-sus delayed second dose vaccination prioritizing the firstdose. Sensitivity analyses included first dose vaccine effi-cacy of 50%, 60%, 70%, 80%, and 90% after day 12 post-vaccination with a vaccination rate of 0.3% population perday; assuming the vaccine prevents only symptoms but notasymptomatic spread (that is, non-sterilizing vaccine). Wemeasure cumulative covid-19 mortality, cumulative SARS-CoV-2 infections, and cumulative hospital admissions due tocovid-19 over 74 days. We explicitly modeled the confirma-tion of infections with polymerase chain reaction testing andquarantining of known infected agents with imperfect com-pliance over time. To simulate a natural pattern of infectionat the point vaccinations begin, we started our simulationwith 10 agents infected and ran the simulation for 20 daysbefore starting vaccinations, which corresponds to a cumu-lative infection rate of 1%, similar to the one in the US,

his performance efficiencycan be attributed to the design of a sparse tensor-calculusbased implementation of GRADABM.

transfer learning from joint county training.

faster than prior-art.

Thus, we opted to use the same set of ABM parameters forevery 7 days (i.e., we learn a new set of parameters for everyweek).

nstead we use transfer learning inGRADABM to learn a single CALIBNN that can predictfor all counties.

TL

he ground truth data forthe target variables is obtained from JHU and CDC.

Safegraph

llow

optimized usinggradient

These unseen sce-narios may include predicting future the evolution of multi-ple infections for a county/region, or it may involve makingpredictions for a new county/region for which historical datafor calibration is not available, or it may involve makingpredictions even when the data (inputs to CALIBNN) for acounty/region is noisy. I

predicting future the evolut

The Transmission Model is differentiable as the functionscomprising it, which are: λ is a smooth function, ⋃ is apermutation invariant function (∑) and is linear.

ontinued till an

estimate gradient

he output of GRADABM is aggregated to compute cumula-tive deaths. This macro value is compared with correspond-ing ground truth values and the following loss is computed:L(ˆyw, y; (θtT , θtP )w) = MSE(ˆyw, y),

at the the

is determines a

here Update(Xti , Ni, (Xtj )j∈Ni , θtT , θtP ) is={Transmit(Xti , Ni, (Xtj )j∈Ni , θtT ), if dti = S,Progress(Xti , θtP ), if dti ∈ {E, I

s. The inputto the simulator are the time-dependent parameters whichgovern the transmission and progression models, denotedas θtT = [Rt, S, T ], θtP = [m, τEI , τIR, τIM ] respectively

They key difference between our model and the SEIRM likemodels is that we track states of individual agents ratherthan just the aggregate numbers of agents in various dis-eases stages. Furthermore, we model the S → E exposurestep, using interaction networks which take into accountlocal agent interactions, which is different from the standardSEIRM like models.

the SEIRM like

Differentiable agent-based epidemiological modeling for end-to-end learning

The probability of transmission (q(.; .)) from the interactionis represented as: q(dti, dtj ) = 1 − e−λ(R,Si,Tj ,∆Etj ), where,λ(R, Si, Tj , ∆Etj ) = RSiTjˆIi∫ ∆Etj∆Etj −1 GΓ(u; μj , σ2j )d

ˆIi is theexpected number of interactions for agent i

is modeled using a gamma distribution

dtj ∈ {0, . . . t − 1}respectively.

micro loop

can be imple-mented a variant of message passi

ferentiable agent-based

we observethat epidemiological models ( 22 ; 36 ; 4; 53 ) also adhere topermutation invariance wherein the order of infectious in-teractions (pair-wise message passing) within a step doesnot matter when estimating the probability of infection fromthose interactions.

We posit that while useful for learning DNNs, utilizing theseinvariances can make computation tractable in physical sys-tems, where they exist naturally

Efficacy of DNNarchitectures results from overcoming the curse of dimen-sionality by leveraging the pre-defined invariances arisingfrom the underlying low-dimensionality and structure of thephysical world (17 ).

There been attempts to reduce thisburden and simulate realistic scale with distributed HPCsystems and GPU-optimized implementations.

here been attempts to re

while ease to us

Conventional frameworks like Mesa

n contrast, the differentiable design of GRADABMallows to calibrate parameters with gradient-based optimiza-tion inside the ABM itself. This helps learn personalizedparameters resulting in better (and robust) forecasting andpolicy decision making.

Recent worksis using optimization methods

conducted by offline by clinical experts

6. DiscussionWe introduce GRADABM, a differentiable ABM that cansimulate million-scale populations in few seconds on com-modity hardware and be merged with DNNs for end-to-endlearning. The key idea of GRADABM is a general-purposedifferentiable sparse tensor-calculus based implementationwhich we validate for epidemiology here. We demonstrateutility of GRADABM to learn personalized time-varyingparameters using heterogeneous data sources to better in-form forecasting and policy decision making. Future workcould explore other benefits like the incorporation of mul-tiple hierarchies of data (also known as macro-micro pre-dictions (64 )). In our experiments, we found that even withsparse optimization, GRADABM utilizes a high amount ofCPU/GPU memory (especially in the backward computa-tion) which could be an issue for simulations of 6+ months.Addressing this limitation could be an interesting futuredirection. Our ABM used a a linear deterministic model forthe disease progression. Future work could explore how toincorporate more complex and stochastic disease progres-sion models (e.g., (53))

Our Contributions: (i) We present GRADABM, a differen-tiable ABM that can simulate million-scale populations infew seconds on commodity hardware and be merged withDNNs for end-to-end learning. The key idea of GRADABMis a general-purpose differentiable sparse tensor-calculusbased implementation which we validate for epidemiologyhere. (ii) We demonstrate utility of GRADABM for robustforecasting and analysis of COVID-19 and Influenza. (iii)We show the use of GRADABM in evaluating pharmaceuti-cal interventions for policy decision making

agents are represented as tensors,their interaction networks as (sparse) adjacency matricesand a continuous relaxation of the stochastic disease trans-mission model is used to produce gradient estimates withautomatic differentiation.

However, they are conven-tionally slow, difficult to scale to large population sizes ( 45 )and tough to calibrate with real-world data (29). This is achallenge since simulation results (emergent behavior) canbe highly sensitive to the scale of the input population andcalibration of the input parameters. In addition, incorporat-ing novel sources of data that could inform calibration andother downstream tasks (e.g., forecasting) is often laboriousand adds overhead complexity to the ABM (e.g., incorpo-rating digital exposure data to ABMs ( 36 )). In this paper,we introduce GRADABM to alleviate these concerns

Mechanistic simulators are an indispensable tool for epi-demiology to explore the behavior of complex, dynamicinfections under varying conditions and navigate uncer-tain environments. ODE-based models are the dominantparadigm that enable fast simulations and are tractable togradient-based optimization, but make simplifying assump-tions about population homogeneity. Agent-based models(ABMs) are an increasingly popular alternative paradigmthat can represent the heterogeneity of contact interactionswith granular detail and agency of individual behavior. How-ever, conventional ABM frameworks are not differentiableand present challenges in scalability; due to which it is non-trivial to connect them to auxiliary data sources easily. Inthis paper we introduce GRADABM which is a new scal-able, fast and differentiable design for ABMs. GRADABMruns simulations in few seconds on commodity hardwareand enables fast forward and differentiable inverse simu-lations. This makes it amenable to be merged with deepneural networks and seamlessly integrate heterogeneousdata sources to help with calibration, forecasting and policyevaluation. We demonstrate the efficacy of GRADABM viaextensive experiments with real COVID-19 and influenzadatasets. We are optimistic this work will bring ABM andAI communities closer together.

optimistic this work willbring ABM and AI communities closer together.

demonstrate the efficacy of GRADABM via ex-tensive experiments with real COVID-19 and in-fluenza datase

merged with deep neural networks and seamlesslyintegrate heterogeneous data sources to help withcalibration, forecasting and policy evaluation.

GRAD-ABM which is a new scalable, fast and differen-tiable design for ABMs. GRADABM runs sim-ulations in few seconds on commodity hardwareand enables fast forward and differentiable in-verse simulations

However, conven-tional ABM frameworks are not differentiable andpresent challenges in scalability; due to which itis non-trivial to connect them to auxiliary datasources easily.

‘subreddit categorization’

The share of views allocated to misleading con-tent promoted via coordinated activity relative to thecounterfactual scenario

The content diversity or the variance of all rec-ommended content at each timestep to measure thedegree of homogenization of visible content similar to(Chaney et al., 2018; Lucherini et al., 2021)

In thispaper we propose to model two popular patterns of coor-dinated activity and present preliminary results from thefirst

generalize the components ofour simulator to different social media platforms to describehow our software serves as a framework for analyzing theimpact of coordinated attacks on end-users of any of theseplatforms

conduct a comparative study ofrisk-quantification conditional upon choice of recommen-dation algorithm.

Weadopt information-theoretic definitions similar to (Lucheriniet al., 2021) to quantify the harms arising from coordinatedinauthentic behavior

metricsthat can be manipulated through coordinated activity includ-ing fake profiles and illicit collusion

We expect thatthis will inform the design of robust content distri-bution systems that are resilient against targetedattacks by groups of malicious actors

collect millions ofreal-world interactions from Reddit to estimatethe network for each user in our dataset and utiliseReddit’s self-described content ranking strategiesto compare the impact of coordinated activity oncontent spread by each strateg

Wedevelop a multiagent simulation of a popular so-cial network, Reddit, that aligns with the state-action space available to real users based on theplatform’s affordances.

simulations have emerged as a populartechnique to study the long-term effects of con-tent ranking and recommendation systems

it isunclear how effective countermeasures to disinfor-mation are in practice due to the limited view wehave into the operation of such platforms

he vulnerabil-ity of ranking and recommendation algorithmsto attack from coordinated campaigns spreadingmisleading information has been established boththeoretically and anecdotally

After N attackers contribute private datasets Di to jointdataset D,

To achieve this attack objective,a common attack vector is through that of outsourced datacollection

n this work, we evaluate existing single-agent back-door defenses to find that they cannot increase the accuracyw.r.t. clean labels during a backdoor attack, and furthermorecontribute three multi-agent backdoor defenses motivatedby agent dynamics. In addition, we are among the firstto construct multi-distributional subspaces to tackle jointdistribution shifts.

This yieldsa side-effect of low accuracy w.r.t. clean labels,which motivates

multi-agent backdoorattack

this paper’s work on the construc-tion of multi-agent backdoor defenses that max-imize accuracy w.r.t. clean labels and minimizethat of poison labels.

the backfiring effect, a natu-ral defense against backdoor attacks where back-doored inputs are randomly classified