We study a class of bilevel optimization problems in which both the upper- and lower-level problems have minimax structures. This setting captures a broad range of emerging applications. Despite the extensive literature on bilevel optimization and minimax optimization separately, existing methods mainly focus on bilevel optimization with lower-level minimization problems, often under strong convexity assumptions, and are not directly applicable to the minimax lower-level setting considered here. To address this gap, we develop penalty-based first-order methods for bilevel minimax optimization without requiring strong convexity of the lower-level problem. In the deterministic setting, we establish that the proposed method finds an $ε$-KKT point with $\tilde{O}(ε^{-4})$ oracle complexity. We further show that bilevel problems with convex constrained lower-level minimization can be reformulated as special cases of our framework via Lagrangian duality, leading to an $\tilde{O}(ε^{-4})$ complexity bound that improves upon the existing $\tilde{O}(ε^{-7})$ result. Finally, we extend our approach to the stochastic setting, where only stochastic gradient oracles are available, and prove that the proposed stochastic method finds a nearly $ε$-KKT point with $\tilde{O}(ε^{-9})$ oracle complexity.

Distributional treatment effects can be invisible to means: a treatment may preserve average outcomes while changing tails, modes, dispersion, or rare-event probabilities. Kernel tests can detect discrepancies between interventional outcome laws, but global tests do not reveal where the laws differ. We propose DR-ME, to our knowledge the first semiparametrically efficient finite-location test for interpretable distributional treatment effects. DR-ME evaluates an interventional kernel witness at learned outcome locations, returning causal-discrepancy coordinates rather than only a global rejection. From observational data, we derive orthogonal doubly robust kernel features whose centered oracle form is the canonical gradient of this finite witness. For fixed locations, we characterize the local testing limit: DR-ME is chi-square calibrated under the null, has noncentral chi-square local power, and uses the covariance whitening that optimizes local signal-to-noise for discrepancies visible through the selected coordinates. This efficient local-power geometry yields a principled location-learning criterion, with sample splitting preserving post-selection validity. Experiments show near-nominal type-I error, competitive power against global doubly robust kernel tests, and interpretable learned locations that localize distributional effects in a semi-synthetic medical-imaging study.

Asteroseismology is the study of resonant oscillations of stars to infer their internal structure and dynamics. It is also a powerful tool for precisely determining stellar parameters such as mass, radius, surface gravity, and age. The ongoing TESS mission, with its nearly complete sky coverage, presents a unique opportunity to uniformly probe stellar populations across the Milky Way. TESS is estimated to have observed more than 300,000 oscillating red giants, most of which have one to two months of observations. Given the scale of this dataset, we need a fast, efficient, and robust way to analyse the data. In this work, our objective is to develop a machine learning (ML) based method to infer asteroseismic parameters from short-duration observations. Specifically, we focus on two global seismic parameters, the large frequency separation ($Δν$) and the frequency at maximum power ($ν_{\mathrm{max}}$), from one-month-long TESS observations of red giants. Meanwhile, for K2 data, our focus extends to inferring the period spacings of dipolar gravity modes ($ΔΠ_{1}$), in addition to $Δν$ and $ν_{\mathrm{max}}$. Our findings demonstrate that our machine learning algorithm can accurately infer $Δν$ and $ν_{\mathrm{max}}$ for approximately 50% of samples created by taking one-month Kepler and K2 observations. For TESS one sector data however, we recover reliable $Δν$ for only about 23% of the stars. Additionally, we get reliable $ΔΠ_{1}$ inferences for about 200 young red-giants from K2. For these $ΔΠ_{1}$ inferences, we see a good match with the well known $Δν-ΔΠ_{1}$ degenerate sequence observed in Kepler red-giants.

$L_1$-Approximating polynomials, i.e., polynomials that approximate indicator functions in $L_1$-norm under certain distributions, are widely used in computational learning theory. We study the existence of \textit{non-negative} $L_1$-approximating polynomials with respect to Gaussian distributions. This is a stronger requirement than $L_1$-approximation but weaker than sandwiching polynomials (which themselves have many applications). These non-negative approximating polynomials have recently found uses in smoothed learning from positive-only examples. In this short note, we prove that every class of sets with Gaussian surface area (GSA) at most $Γ$ under the standard Gaussian admits degree-$k$ non-negative polynomials that $\eps$-approximate its indicator functions in $L_1$-norm, for $k=\tilde{O}(Γ^2/\varepsilon^2)$. Equivalently, finite GSA implies $L_1$-approximation with the stronger pointwise guarantee that the approximating polynomial has range contained in $[0,\infty)$. Up to a constant-factor, this matches the degree of the best currently known Gaussian $L_1$-approximation degree bound without the non-negativity constraint.

Death of Alabama woman, 22, 'accidentally' shot in chest by boyfriend's dad is ruled a HOMICIDE Two small airlines join forces to create America's newest budget carrier after Spirit collapse leaves millions scrambling Horrifying final days of killer dad Chris Watts' pregnant wife before she was slaughtered alongside their daughters. Read all the chilling texts and receipts in full for first time: 'My eyes burn from crying' I'm a pastor who attended a secret UFO disclosure meeting. We saw images of'translucent beings' that chilled me to the bone... the files could fulfil a dark biblical prophecy Former NFL player Josh Mauro's tragic cause of death revealed after league was left'devastated' by ex-Cardinals and Giants man's sudden passing at 35 Cheerful Christian mom is pillar of Florida community and loves going on TV... but she has a childhood secret so evil that she stuttered with shock when confronted with it Taxpayers to foot Trump's $1.7 BILLION bill as President sues his own government: 'I'm paying myself' How I lost 3 STONE in 3 WEEKS. I've reversed pre-diabetes and no longer need a knee op: DONAL MACINTYRE's extraordinary investigation Popular megachurch in crisis as senior pastor suddenly quits... as bosses furiously DENY sex scandal Husband of doomed dive group leader says'something must have happened down there' as mystery surrounds why the five attempted to explore'cave so deep even divers with best equipment don't try' Greeks savage Kimberly Guilfoyle as Trump's ambassador opens McDonald's in country celebrated for world-class food Trump touts'fantastic' China trade win on Air Force One... but Wall Street is punishing the President I'm godfather to Candace Owens' daughter and Charlie Kirk was my friend... so I know the real reason she's attacking Erika - and I'll never publicly condemn her Wealthy dad'snarled the worst thing a parent could say' to younger daughter before he allegedly executed wife outside their gated community home during nightmare divorce Reese Witherspoon and Ryan Phillippe reunite for son's NYU graduation... as Kate Hudson cheers on her boy at same ceremony with Goldie Hawn and Kurt Russell'How do you live with that?' Disgraced Eric Swalwell's'blindsided' wife dresses for revenge... as friends reveal brutal toll sex assault scandal has had on young mom Judge declares another mistrial in disgraced Hollywood mogul Harvey Weinstein's rape case Can't lose weight no matter what you do? These are the 7 surprising reasons why, including'healthy' hacks actually making you put on pounds.

Flytrex has partnered with Little Caesars to deliver full pizza orders by drone in Wylie, Texas, with food arriving in roughly four and a half minutes.

What are Russia's gains from the Iran war? 'We are not losers; we are winners' At least three people have been killed in Russian attacks on Ukraine in the past 24 hours despite a three-day ceasefire announced by US President Donald Trump that came into effect on May 9. Regional authorities on Sunday reported one death each in Ukraine's Zaporizhia, Dnipropetrovsk, and Kherson regions. Governor Oleksandr Prokudin confirmed the death on Telegram, saying the woman had been struck while walking down the street. Seven people, including a child, have also been injured across the region in drone or artillery attacks since early Saturday, he added. Ivan Fedorov, the governor of the southeastern Zaporizhia region, said one person had been killed and three others injured by artillery and drone attacks in the past 24 hours. In the northeastern Kharkiv region, Governor Oleh Syniehubov said eight people, including two children, were injured in drone attacks on the city of Kharkiv and nearby settlements.

I knew my writing students were using AI. It's what's lost when we surrender the struggle to translate thought into words I have been teaching fiction writing at MIT since 2017. Mark what works and what doesn't - underline great sentences, flag clunky syntax, gaps in logic and unrealistic dialogue. Ask yourself: does the story work? Answer in a signed letter to the author, attached to their story.

How well do you know Iran? A fragile ceasefire in the US-Israel war on Iran is coming under growing strain as several Gulf countries have reported drone attacks. Qatar said on Sunday that a drone struck a cargo ship in Qatari waters, sparking a fire, while Kuwait and the United Arab Emirates said they repelled drone attacks. Qatar's Ministry of Defence said the freighter had been arriving in the country's waters from the UAE capital, Abu Dhabi, and was hit by a drone northeast of the port of Mesaieed. "The vessel continued its journey toward Mesaieed Port after the fire was brought under control," the ministry said. The United Kingdom Maritime Trade Operations (UKMTO) said a bulk carrier reported being struck by an "unknown projectile", and a small fire had been extinguished, but there were no casualties from the incident.

A member of NOPO, Iran's counter-terrorism special force, stands guard under a billboard of Iran's late supreme leader, Ayatollah Ali Khamenei, in Tehran, on April 23. Doha - A drone struck a commercial vessel in Qatari waters on Sunday, the country's defense ministry said, after Iran's Islamic Revolutionary Guards threatened to target U.S. vessels in the region. Arch-foes the United States and Iran have been clashing in the Gulf and trading accusations in recent days, as Washington waits for Tehran to respond to its latest negotiating position. A commercial cargo vessel in the country's territorial waters -- northeast of Mesaieed Port -- coming from Abu Dhabi, was targeted by a drone on Sunday morning. The incident resulted in a limited fire on board the vessel, with no reported injuries, the Qatari ministry said on X.