Is Knowledge Power? On the (Im)possibility of Learning from Strategic Interaction

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.

Truthfulness of Calibration Measures

We initiate the study of the truthfulness of calibration measures in sequential prediction. A calibration measure is said to be truthful if the forecaster (approximately) minimizes the expected penalty by predicting the conditional expectation of the next outcome, given the prior distribution of outcomes. Truthfulness is an important property of calibration measures, ensuring that the forecaster is not incentivized to exploit the system with deliberate poor forecasts. This makes it an essential desideratum for calibration measures, alongside typical requirements, such as soundness and completeness. We conduct a taxonomy of existing calibration measures and their truthfulness. Perhaps surprisingly, we find that all of them are far from being truthful. That is, 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. Our main contribution is the introduction of a new calibration measure termed the Subsampled Smooth Calibration Error (SSCE) under which truthful prediction is optimal up to a constant multiplicative factor.

Covert Malicious Finetuning: Challenges in Safeguarding LLM Adaptation

Black-box finetuning is an emerging interface for adapting state-of-the-art language models to user needs. However, such access may also let malicious actors undermine model safety. To demonstrate the challenge of defending finetuning interfaces, we introduce covert malicious finetuning, a method to compromise model safety via finetuning while evading detection. Our method constructs a malicious dataset where every individual datapoint appears innocuous, but finetuning on the dataset teaches the model to respond to encoded harmful requests with encoded harmful responses. Applied to GPT-4, our method produces a finetuned model that acts on harmful instructions 99% of the time and avoids detection by defense mechanisms such as dataset inspection, safety evaluations, and input/output classifiers. Our findings question whether black-box finetuning access can be secured against sophisticated adversaries.

Can Probabilistic Feedback Drive User Impacts in Online Platforms?

A common explanation for negative user impacts of content recommender systems is misalignment between the platform's objective and user welfare. In this work, we show that misalignment in the platform's objective is not the only potential cause of unintended impacts on users: even when the platform's objective is fully aligned with user welfare, the platform's learning algorithm can induce negative downstream impacts on users. The source of these user impacts is that different pieces of content may generate observable user reactions (feedback information) at different rates; these feedback rates may correlate with content properties, such as controversiality or demographic similarity of the creator, that affect the user experience. Since differences in feedback rates can impact how often the learning algorithm engages with different content, the learning algorithm may inadvertently promote content with certain such properties. Using the multi-armed bandit framework with probabilistic feedback, we examine the relationship between feedback rates and a learning algorithm's engagement with individual arms for different no-regret algorithms. We prove that no-regret algorithms can exhibit a wide range of dependencies: if the feedback rate of an arm increases, some no-regret algorithms engage with the arm more, some no-regret algorithms engage with the arm less, and other no-regret algorithms engage with the arm approximately the same number of times. From a platform design perspective, our results highlight the importance of looking beyond regret when measuring an algorithm's performance, and assessing the nature of a learning algorithm's engagement with different types of content as well as their resulting downstream impacts.

Smooth Nash Equilibria: Algorithms and Complexity

A fundamental shortcoming of the concept of Nash equilibrium is its computational intractability: approximating Nash equilibria in normal-form games is PPAD-hard. In this paper, inspired by the ideas of smoothed analysis, we introduce a relaxed variant of Nash equilibrium called $\sigma$-smooth Nash equilibrium, for a smoothness parameter $\sigma$. In a $\sigma$-smooth Nash equilibrium, players only need to achieve utility at least as high as their best deviation to a $\sigma$-smooth strategy, which is a distribution that does not put too much mass (as parametrized by $\sigma$) on any fixed action. We distinguish two variants of $\sigma$-smooth Nash equilibria: strong $\sigma$-smooth Nash equilibria, in which players are required to play $\sigma$-smooth strategies under equilibrium play, and weak $\sigma$-smooth Nash equilibria, where there is no such requirement. We show that both weak and strong $\sigma$-smooth Nash equilibria have superior computational properties to Nash equilibria: when $\sigma$ as well as an approximation parameter $\epsilon$ and the number of players are all constants, there is a constant-time randomized algorithm to find a weak $\epsilon$-approximate $\sigma$-smooth Nash equilibrium in normal-form games. In the same parameter regime, there is a polynomial-time deterministic algorithm to find a strong $\epsilon$-approximate $\sigma$-smooth Nash equilibrium in a normal-form game. These results stand in contrast to the optimal algorithm for computing $\epsilon$-approximate Nash equilibria, which cannot run in faster than quasipolynomial-time. We complement our upper bounds by showing that when either $\sigma$ or $\epsilon$ is an inverse polynomial, finding a weak $\epsilon$-approximate $\sigma$-smooth Nash equilibria becomes computationally intractable.

Delegating Data Collection in Decentralized Machine Learning

Motivated by the emergence of decentralized machine learning ecosystems, we study the delegation of data collection. Taking the field of contract theory as our starting point, we design optimal and near-optimal contracts that deal with two fundamental machine learning challenges: lack of certainty in the assessment of model quality and lack of knowledge regarding the optimal performance of any model. We show that lack of certainty can be dealt with via simple linear contracts that achieve 1-1/e fraction of the first-best utility, even if the principal has a small test set. Furthermore, we give sufficient conditions on the size of the principal's test set that achieves a vanishing additive approximation to the optimal utility. To address the lack of a priori knowledge regarding the optimal performance, we give a convex program that can adaptively and efficiently compute the optimal contract.

The Sample Complexity of Multi-Distribution Learning for VC Classes

Multi-distribution learning is a natural generalization of PAC learning to settings with multiple data distributions. There remains a significant gap between the known upper and lower bounds for PAC-learnable classes. In particular, though we understand the sample complexity of learning a VC dimension d class on $k$ distributions to be $O(\epsilon^{-2} \ln(k)(d + k) + \min\{\epsilon^{-1} dk, \epsilon^{-4} \ln(k) d\})$, the best lower bound is $\Omega(\epsilon^{-2}(d + k \ln(k)))$. We discuss recent progress on this problem and some hurdles that are fundamental to the use of game dynamics in statistical learning.

Jailbroken: How Does LLM Safety Training Fail?

Large language models trained for safety and harmlessness remain susceptible to adversarial misuse, as evidenced by the prevalence of "jailbreak" attacks on early releases of ChatGPT that elicit undesired behavior. Going beyond recognition of the issue, we investigate why such attacks succeed and how they can be created. We hypothesize two failure modes of safety training: competing objectives and mismatched generalization. Competing objectives arise when a model's capabilities and safety goals conflict, while mismatched generalization occurs when safety training fails to generalize to a domain for which capabilities exist. We use these failure modes to guide jailbreak design and then evaluate state-of-the-art models, including OpenAI's GPT-4 and Anthropic's Claude v1.3, against both existing and newly designed attacks. We find that vulnerabilities persist despite the extensive red-teaming and safety-training efforts behind these models. Notably, new attacks utilizing our failure modes succeed on every prompt in a collection of unsafe requests from the models' red-teaming evaluation sets and outperform existing ad hoc jailbreaks. Our analysis emphasizes the need for safety-capability parity -- that safety mechanisms should be as sophisticated as the underlying model -- and argues against the idea that scaling alone can resolve these safety failure modes.

Improved Bayes Risk Can Yield Reduced Social Welfare Under Competition

As the scale of machine learning models increases, trends such as scaling laws anticipate consistent downstream improvements in predictive accuracy. However, these trends take the perspective of a single model-provider in isolation, while in reality providers often compete with each other for users. In this work, we demonstrate that competition can fundamentally alter the behavior of these scaling trends, even causing overall predictive accuracy across users to be non-monotonic or decreasing with scale. We define a model of competition for classification tasks, and use data representations as a lens for studying the impact of increases in scale. We find many settings where improving data representation quality (as measured by Bayes risk) decreases the overall predictive accuracy across users (i.e., social welfare) for a marketplace of competing model-providers. Our examples range from closed-form formulas in simple settings to simulations with pretrained representations on CIFAR-10. At a conceptual level, our work suggests that favorable scaling trends for individual model-providers need not translate to downstream improvements in social welfare in marketplaces with multiple model providers.

Calibrated Stackelberg Games: Learning Optimal Commitments Against Calibrated Agents

In this paper, we introduce a generalization of the standard Stackelberg Games (SGs) framework: Calibrated Stackelberg Games (CSGs). 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 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.