Strategic classification addresses a learning problem where a decision-maker implements a classifier over agents who may manipulate their features in order to receive favorable predictions. In the standard model of online strategic classification, in each round, the decision-maker implements and publicly reveals a classifier, after which agents perfectly best respond based on this knowledge. However, in practice, whether to disclose the classifier is often debated—some decision-makers believe that hiding the classifier can prevent misclassification errors caused by manipulation. In this paper, we formally examine how limiting the agents’ access to the current classifier affects the decision-maker’s performance. Specifically, we consider an extended online strategic classification setting where agents lack direct knowledge about the current classifier and instead manipulate based on a weighted average of historically implemented classifiers. Our main result shows that in this setting, the decision-maker incurs $(1-\gamma)^{-1}$ or $k_{\text{in}}$ times more mistakes compared to the full-knowledge setting, where $k_{\text{in}}$ is the maximum in-degree of the manipulation graph (representing how many distinct feature vectors can be manipulated to appear as a single one), and $\gamma$ is the discount factor indicating agents’ memory of past classifiers. Our results demonstrate how withholding access to the classifier can backfire and degrade the decision-maker’s performance in online strategic classification.

After pre-training, large language models are aligned with human preferences based on pairwise comparisons. State-of-the-art alignment methods (such as PPO-based RLHF and DPO) are built on the assumption of aligning with a single preference model, despite being deployed in settings where users have diverse preferences. As a result, it is not even clear that these alignment methods produce models that satisfy users \emph{on average} --- a minimal requirement for pluralistic alignment. Drawing on social choice theory and modeling users' comparisons through individual Bradley-Terry (BT) models, we introduce an alignment method's \emph{distortion}: the worst-case ratio between the optimal achievable average utility, and the average utility of the learned policy. The notion of distortion helps draw sharp distinctions between alignment methods: \emph{Nash Learning from Human Feedback} achieves the minimax optimal distortion of $(\frac{1}{2} + o(1)) \cdot \beta$ (for the BT temperature $\beta$), robustly across utility distributions, distributions of comparison pairs, and permissible KL divergences from the reference policy. RLHF and DPO, by contrast, suffer $\geq (1 - o(1)) \cdot \beta$ distortion already without a KL constraint, and $e^{\Omega(\beta)}$ or even unbounded distortion in the full setting, depending on how comparison pairs are sampled.

This paper introduces the concept of leakage-robust Bayesian persuasion. Situated between public Bayesian persuasion and private Bayesian persuasion, leakage-robust persuasion considers a setting where one or more signals privately communicated by a sender to the receivers may be leaked. We study the design of leakage-robust Bayesian persuasion schemes and quantify the price of robustness using two formalisms:

Collaboration is crucial for reaching collective goals. However, its potential for effectiveness is often undermined by the strategic behavior of individual agents — a fact that is captured by a high Price of Stability (PoS) in recent literature [BHPS21]. Implicit in the traditional PoS analysis is the assumption that agents have full knowledge of how their tasks relate to one another. We offer a new perspective on bringing about efficient collaboration across strategic agents using information design. Inspired by the increasingly important role collaboration plays in machine learning (such as platforms for collaborative federated learning and data cooperatives), we propose a framework in which the platform possesses more information about how the agents’ tasks relate to each other than the agents themselves. Our results characterize how and to what degree such platforms can leverage their information advantage and steer strategic agents towards efficient collaboration.

We study the problem of online binary classification in settings where strategic agents can modify their observable features to receive a positive classification. We model the set of feasible manipulations by a directed graph over the feature space, and assume the learner only observes the manipulated features instead of the original ones. We introduce the Strategic Littlestone Dimension, a new combinatorial measure that captures the joint complexity of the hypothesis class and the manipulation graph. We demonstrate that it characterizes the instance-optimal mistake bounds for deterministic learning algorithms in the realizable setting. We also achieve improved regret in the agnostic setting by a refined agnostic-to-realizable reduction that accounts for the additional challenge of not observing agents' original features. Finally, we relax the assumption that the learner knows the manipulation graph, instead assuming their knowledge is captured by a family of graphs. We derive regret bounds in both the realizable setting where all agents manipulate according to the same graph within the graph family, and the agnostic setting where the manipulation graphs are chosen adversarially and not consistently modeled by a single graph in the family.

When learning in strategic environments, a key question is whether agents can overcome uncertainty about their preferences to achieve outcomes they could have achieved absent any uncertainty. Can they do this solely through interactions with each other? We focus this question on the ability of agents to attain the value of their Stackelberg optimal strategy and study the impact of information asymmetry. We study repeated interactions in fully strategic environments where players' actions are decided based on learning algorithms that take into account their observed histories and knowledge of the game. We study the pure Nash equilibria (PNE) of a meta-game where players choose these algorithms as their actions. We demonstrate that if one player has perfect knowledge about the game, then any initial informational gap persists. That is, while there is always a PNE in which the informed agent achieves her Stackelberg value, there is a game where no PNE of the meta-game allows the partially informed player to achieve her Stackelberg value. On the other hand, if both players start with some uncertainty about the game, the quality of information alone does not determine which agent can achieve her Stackelberg value. In this case, the concept of information asymmetry becomes nuanced and depends on the game's structure. Overall, our findings suggest that repeated strategic interactions alone cannot facilitate learning effectively enough to earn an uninformed player her Stackelberg value.

We study calibration measures in a sequential prediction setup. In addition to rewarding accurate predictions (completeness) and penalizing incorrect ones (soundness), an important desideratum of calibration measures is *truthfulness*, a minimal condition for the forecaster not to be incentivized to exploit the system. Formally, a calibration measure is truthful if the forecaster (approximately) minimizes the expected penalty by predicting the conditional expectation of the next outcome, given the prior distribution of outcomes. We conduct a taxonomy of existing calibration measures. Perhaps surprisingly, all of them are far from being truthful. We introduce a new calibration measure termed the *Subsampled Smooth Calibration Error (SSCE)*, which is complete and sound, and under which truthful prediction is optimal up to a constant multiplicative factor. In contrast, under existing calibration measures, there are simple distributions on which a polylogarithmic (or even zero) penalty is achievable, while truthful prediction leads to a polynomial penalty.

We study Bayesian persuasion under approximate best response, where the receiver may choose any action that is not too much suboptimal, given their posterior belief upon receiving the signal. We focus on the computational aspects of the problem, aiming to design algorithms that efficiently compute (almost) optimal strategies for the sender. Despite the absence of the revelation principle --- which has been one of the most powerful tools in Bayesian persuasion --- we design polynomial-time exact algorithms for the problem when either the state space or the action space is small, as well as a quasi-polynomial-time approximation scheme (QPTAS) for the general problem. On the negative side, we show there is no polynomial-time exact algorithm for the general problem unless $\mathsf{P} = \mathsf{NP}$. Our results build on several new algorithmic ideas, which might be useful in other principal-agent problems where robustness is desired.

In this paper, we introduce a generalization of the standard Stackelberg Games (SGs) framework: _Calibrated Stackelberg Games_. In CSGs, a principal repeatedly interacts with an agent who (contrary to standard SGs) does not have direct access to the principal's action but instead best responds to _calibrated forecasts_ about it. CSG is a powerful modeling tool that goes beyond assuming that agents use ad hoc and highly specified algorithms for interacting in strategic settings to infer the principal's actions and thus more robustly addresses real-life applications that SGs were originally intended to capture. Along with CSGs, we also introduce a stronger notion of calibration, termed _adaptive calibration_, that provides fine-grained any-time calibration guarantees against adversarial sequences. We give a general approach for obtaining adaptive calibration algorithms and specialize them for finite CSGs. In our main technical result, we show that in CSGs, the principal can achieve utility that converges to the optimum Stackelberg value of the game both in _finite_ and _continuous_ settings and that no higher utility is achievable. Two prominent and immediate applications of our results are the settings of learning in Stackelberg Security Games and strategic classification, both against _calibrated_ agents.

We study the problem of online binary classification where strategic agents can manipulate their observable features in predefined ways, modeled by a manipulation graph, in order to receive a positive classification. We show this setting differs in fundamental ways from classic (non-strategic) online classification. For instance, whereas in the non-strategic case, a mistake bound of ln |H| is achievable via the halving algorithm when the target function belongs to a known class H, we show that no deterministic algorithm can achieve a mistake bound o(Δ) in the strategic setting, where Δ is the maximum degree of the manipulation graph (even when |H| = O(Δ)). We complement this with a general algorithm achieving mistake bound O(Δ ln |H|). We also extend this to the agnostic setting, and show that this algorithm achieves a Δ multiplicative regret (mistake bound of O(Δ · OPT + Δ · ln |H|)), and that no deterministic algorithm can achieve o(Δ) multiplicative regret.

We study the design of computationally efficient online learning algorithms under smoothed analysis. In this setting, at every step, an adversary generates a sample from an adaptively chosen distribution whose density is upper bounded by $1/\sigma$ times the uniform density. Given access to an offline optimization (ERM) oracle, we give the first computationally efficient online algorithms whose sublinear regret depends only on the pseudo/VC dimension $d$ of the class and the smoothness parameter $\sigma$. In particular, we achieve \emph{oracle-efficient} regret bounds of $ O ( \sqrt{T d\sigma^{-1}} ) $ for learning real-valued functions and $ O ( \sqrt{T d\sigma^{-\frac{1}{2}} } )$ for learning binary-valued functions. Our results establish that online learning is computationally as easy as offline learning, under the smoothed analysis framework. This contrasts the computational separation between online learning with worst-case adversaries and offline learning established by [HK16].Our algorithms also achieve improved bounds for some settings with binary-valued functions and worst-case adversaries. These include an oracle-efficient algorithm with $O ( \sqrt{T(d |\mathcal{X}|)^{1/2} })$ regret that refines the earlier $O ( \sqrt{T|\mathcal{X}|})$ bound of [DS16] for finite domains, and an oracle-efficient algorithm with $O(T^{3/4} d^{1/2})$ regret for the transductive setting.

This paper presents the first non-asymptotic result showing a model-free algorithm can achieve logarithmic cumulative regret for episodic tabular reinforcement learning if there exists a strictly positive sub-optimality gap. We prove that the optimistic Q-learning studied in [Jin et al. 2018] enjoys a ${\mathcal{O}}\!\left(\frac{SA\cdot \mathrm{poly}\left(H\right)}{\Delta_{\min}}\log\left(SAT\right)\right)$ cumulative regret bound where $S$ is the number of states, $A$ is the number of actions, $H$ is the planning horizon, $T$ is the total number of steps, and $\Delta_{\min}$ is the minimum sub-optimality gap of the optimal Q-function. This bound matches the information theoretical lower bound in terms of $S,A,T$ up to a $\log\left(SA\right)$ factor. We further extend our analysis to the discounted setting and obtain a similar logarithmic cumulative regret bound.