Many modern decision systems are not passive observers of the world they measure: the decisions they make change the data they subsequently receive. For example, a seller that posts a price influences the decisions of potential buyers, and hence the sales data it goes on to col-
lect; a lender that deploys a credit-scoring rule changes the nature of the loan applications it receives. In such settings, the classical separation
between estimation and decision-making breaks down, and statistical guarantees must be derived jointly with the policy that generates the
data. This dissertation develops estimation theory and online algorithms for two such feedback settings --- dynamic pricing and performative
prediction --- with a unifying theme: shape-constrained and microfounded structure can replace the tuning parameters, smoothness assump-
tions, and parametric models on which existing methods rely.
The first part concerns dynamic pricing. We first consider a monopolistic setting with censored demand, in which the seller posts a price and
observes only whether a sale occurred. In the linear valuation model, the customer’s valuation is linear in the features of the item offered,
up to market noise with unknown distribution F. Existing methods estimate F by kernel smoothing, bandit techniques, or upper confidence
bounds; all of them impose Lipschitz or stronger conditions on F, and all of them leave the analyst to choose bandwidths, confidence widths,
or regularization parameters. We instead exploit the fact that F is monotone and estimate it by isotonic regression. The resulting policy car-
ries no tuning parameters whatsoever, assumes only that F is Hölder continuous, and attains sublinear regret. It also outperforms existing
methods in simulations and on transaction data from Welltower Inc. We then move to a competitive setting in which N sellers post prices
over T periods, and each seller’s demand follows a single-index model with an unknown monotone, s-concave link. We prove existence and
uniqueness of the Nash equilibrium, and give a semiparametric least-squares policy under which prices converge to the Nash equilibrium,
while each seller incurs sublinear regret.
The second part concerns performative prediction, which involves a learner and a population of agents whose actions follow a distribution
P. The learner deploys a model M that shifts this distribution from P to P(M), thereby changing the data the learner observes; the map P(M)
is called the distribution map. Much of the literature assumes that the distribution map is known, whereas we learn it from agent-response
data. We study two settings: a discrete-action framework, in which agents choose from a finite set of alternatives, and a continuous-action
framework, in which an action may be any real number. For discrete actions, we give a nonparametric estimator of the distribution map
together with an exploration--exploitation scheme that we show to be effective in minimizing the performative risk. For continuous actions,
we model agents’ responses as a cost-adjusted utility maximization problem and propose an estimator of the cost. Our approach leverages
optimal transport to align the pre-deployment distribution P with the post-deployment distribution P(M). We provide a rate of convergence
for the proposed estimator and assess its quality through empirical demonstrations on a credit-scoring dataset.