We consider the following two-player game: using observational data, the leader chooses a prediction function for a response variable $Y$ from given covariates. The follower then reacts with an intervention on some covariates in the underlying structural causal model to maximize their own objective. The leader knows the intervention targets, but may have limited knowledge of the follower's objective. We call this setup a prediction-intervention game, a special case of a Stackelberg game. Finding an optimal strategy for the leader is generally difficult. To avoid severe performance loss, the leader may base their prediction on the causal parents of $Y$, or more generally on an invariant subset of covariates. We prove, for two common classes of follower objectives, that predictors based on the stable blanket, a specific invariant subset, are always better or as good as those based on the causal parents. We further upper bound the leader's post-intervention risk by a worst-case risk over allowed interventions and strengthen existing distribution generalization results to analyze this bound: we give sufficient conditions under which stable-blanket predictors are worst-case optimal, and show by examples that these conditions cannot in general be dropped. Finally, we discuss practical strategies for settings with known and unknown graph, and test them on simulated and real-world data.

OnlyFans' First-Gen Creators Are Retiring--and Some Are Begging You to Forget They Exist As more sex workers quit the industry, some are having to navigate tough questions around consent and the "afterlife" of work they no longer want to be associated with. On April 28, just before noon, Win White logged onto X and posted a series of messages to his 65,000 followers who, until that moment, were mostly unaware of his past as an OnlyFans creator. If you see it, save it cool," he wrote . "I know where I've been and I think I'm entitled to a life after that at least." That morning White, 29, had received several DMs about an old clip of him making rounds. Though he has done his best to separate his old life from his new one--last year he deleted his OnlyFans account and the separate X account where he posted content--it often has a habit of catching up with him. "All that work that I did for OnlyFans, I did out in California.

A viral red carpet moment shone light on a group of hunky Instagram influencers--and the followers who are too horny to care that they're not real. With his deep brown eyes, wide grin, and almost comically chiseled body, Jae Young Joon is the platonic ideal of a hunky male influencer. On Instagram, where he has more than 320,000 followers, he regularly posts himself trying on sheet masks at home, enjoying soju and karaoke with his friends, or posing in front of the Ferris wheel at Coachella . Occasionally, he'll promote his music, including his recent LP Pressure Release which features a BDSM-inspired album cover, his back muscles rippling underneath a harness and chains. It's an impressive online presence, and Jae's fans eat it up: his comments are filled with fire and heart-eye emoji and people praising his music.

This Scammer Used an AI-Generated MAGA Girl to Grift'Super Dumb' Men A med student says he's made thousands of dollars selling photos and videos of a young conservative woman he created using generative tools. Like many medical school students, Sam was broke. The 22-year-old aspiring orthopedic surgeon from northern India got some money from his parents, but he says he spent most of it subsidizing his licensing exams, and he's still saving up to hopefully emigrate to the US after graduation. So he started searching for ways to make additional money online. Sam, who requested a pseudonym to avoid jeopardizing his medical career and immigration status, tried a few things, with varying degrees of legitimacy and success.

The optimal policy in various real-world strategic decision-making problems depends both on the environmental configuration and exogenous events. For these settings, we introduce Contextual Bilevel Reinforcement Learning (CB-RL), a stochastic bilevel decision-making model, where the lower level consists of solving a contextual Markov Decision Process (CMDP). CB-RL can be viewed as a Stackelberg Game where the leader and a random context beyond the leader's control together decide the setup of many MDPs that potentially multiple followers best respond to. This framework extends beyond traditional bilevel optimization and finds relevance in diverse fields such as RLHF, tax design, reward shaping, contract theory and mechanism design. We propose a stochastic Hyper Policy Gradient Descent (HPGD) algorithm to solve CB-RL, and demonstrate its convergence. Notably, HPGD uses stochastic hypergradient estimates, based on observations of the followers' trajectories. Therefore, it allows followers to use any training procedure and the leader to be agnostic of the specific algorithm, which aligns with various real-world scenarios. We further consider the setting when the leader can influence the training of followers and propose an accelerated algorithm. We empirically demonstrate the performance of our algorithm for reward shaping and tax design.

Morphology-control co-design concerns the coupled optimization of an agent's body structure and control policy. This problem exhibits a bi-level structure, where the control dynamically adapts to the morphology to maximize performance. Existing methods typically neglect the control's adaptation dynamics by adopting a single-level formulation that treats the control policy as fixed when optimizing morphology. This can lead to inefficient optimization, as morphology updates may be misaligned with control adaptation. In this paper, we revisit the co-design problem from a game-theoretic perspective, modeling the intrinsic coupling between morphology and control as a novel variant of a Stackelberg game. We propose Stackelberg Proximal Policy Optimization (Stackelberg PPO), which explicitly incorporates the control's adaptation dynamics into morphology optimization. By modeling this intrinsic coupling, our method aligns morphology updates with control adaptation, thereby stabilizing training and improving learning efficiency. Experiments across diverse co-design tasks demonstrate that Stackelberg PPO outperforms standard PPO in both stability and final performance, opening the way for dramatically more efficient robotics designs.

The EV manufacturer is supported by a robust online community. But Elon Musk's politics and overblown hype about Full Self-Driving are turning some loyalists away. This month, Tesla customers erupted in outrage over what some called a " bait and switch " by the electric vehicle manufacturer. Initially, the company had offered to transfer the Full Self-Driving feature, which is now only available through a subscription model but could once be purchased for a "lifetime" fee that ran as high as $15,000, to any new Tesla purchased by March 31. The deal was most tempting for drivers already enticed by a new base Cybertruck model that cost just $59,990, a price that CEO Elon Musk soon clarified would only last for 10 days, leaving potential buyers a very small window to make up their minds. Then Tesla quietly amended the language of the FSD transfer agreement, stipulating that customers would need to take delivery of a Tesla by March 31 in order to swap their FSD from their last vehicle to the next.

The optimal policy in various real-world strategic decision-making problems depends both on the environmental configuration and exogenous events.