In this work, we revisit the problem of learning the structure and parameters of an Ising model from dynamics. While the problem of learning from i.i.d. samples has been intensively studied in several communities, recent work has considered learning from temporally correlated samples arising from some stochastic process. However, all prior work studied this problem in the {\em synthetic} observation model that assumes knowledge of internal steps of the standard algorithm for generating samples, which goes far beyond what we should expect to naturally observe from the system evolution in important physics and network applications. Extending these algorithmic guarantees to more realistic observation models has been an important direction highlighted in recent work (Bresler, Gamarnik, Shah IEEE Trans. Inf. Theory 2018, Gaitonde, Moitra, Mossel STOC 2025). We give the first efficient algorithm for learning from the natural continuous-time observation model where we only observe the actual evolution of the state of the system, as opposed to usually unobservable details like failed update attempts of sites. For Ising models with maximum degree $d$, our algorithm first recovers the graph structure in $\mathsf{poly}(d)\cdot n^2\log n$ time, which qualitatively matches the state-of-the-art even in the cleaner i.i.d. setting, and then estimates the parameters in additional $\widetilde{O}(2^d\cdot n)$ time. Our analysis is based on a new family of cycle statistics, which crucially remains measurable for \emph{any} stochastic process, and in fact succeeds more generally for a broad family of reversible, single-site Markov chains that includes both the Glauber dynamics and the Metropolis chain.

A popular method for sampling from high-dimensional distributions is the Gibbs sampler, which iteratively resamples sites from the conditional distribution of the desired measure given the values of the other coordinates. It is natural to ask to what extent does the order of site updates matter in the mixing time? Two popular choices are (i) standard, or random scan, Glauber dynamics where the updated variable is chosen uniformly at random, and (ii) the systematic scan dynamics where variables are updated in a fixed, cyclic order. We first show that for systems of dimension \(n\), one round of the systematic scan dynamics has spectral gap at most a factor of order \(n\) worse than the corresponding spectral gap of a single step of Glauber dynamics, tightening existing bounds in the literature by He, et al. [NeurIPS ’16] and Chlebicka, Łatuszyński, and Miasodejow [Ann. Appl. Probab. ’25]. The corresponding bound on mixing times is sharp even for simple spin systems by an explicit example of Roberts and Rosenthal [Int. J. Statist. Prob. ’15]. We complement this with a converse statement: if all, or even just one scan order rapidly mixes, the Glauber dynamics has a polynomially related mixing time, resolving a question of Chlebicka, Łatuszyński, and Miasodejow.

STOC ’25, Prague, Czechia

We revisit the well-studied problem of efficiently learning the underlying structure and parameters of an Ising model from data. Current algorithmic approaches achieve essentially optimal sample complexity when samples are generated i.i.d. from the stationary measure and the underlying model satisfies ”width” constraints that bound the total ℓ1 interaction involving each node. However, these assumptions are not satisfied in some important settings of interest, like temporally correlated data or more complicated models (like spin glasses) that do not satisfy width bounds.

Online advertising via auctions increasingly dominates the marketing landscape. A typical advertiser may participate in thousands of auctions each day with bids tailored to a variety of signals about user demographics and intent. These auctions are strategically linked through a global budget constraint. To help address the difficulty of bidding, many major online platforms now provide automated budget management via a flexible approach called budget pacing: rather than bidding directly, an advertiser specifies a global budget target and a maximum willingness-to-pay for different types of advertising opportunities. The specified maximums are then scaled down (or "paced") by a multiplier so that the realized total spend matches the target budget. These automated bidders are now near-universally adopted across all mature advertising platforms, raising pressing questions about market outcomes that arise when advertisers use budget pacing simultaneously. In this paper we study the aggregate welfare and individual regret guarantees of dynamic pacing algorithms in repeated auctions with budgets. We show that when agents simultaneously use a natural form of gradient-based pacing, the liquid welfare obtained over the course of the dynamics is at least half the optimal liquid welfare obtainable by any allocation rule, matching the best possible bound for static auctions even in pure Nash equilibria [Aggarwal et al., WINE 2019; Babaioff et al., ITCS 2021]. In contrast to prior work, these results hold without requiring convergence of the dynamics, circumventing known computational obstacles of finding equilibria [Chen et al., EC 2021]. Our result is robust to the correlation structure among agents' valuations and holds for any core auction, a broad class that includes first-price, second-price, and GSP auctions. We complement the aggregate guarantees by showing that an agent using such pacing algorithms achieves an O(T^{3/4}) regret relative to the value obtained by the best fixed pacing multiplier in hindsight in stochastic bidding environments. Compared to past work, this result applies to more general auctions and extends to adversarial settings with respect to dynamic regret.

Bounding the price of anarchy, which quantifies the damage to social welfare due to selfish behavior of the participants, has been an important area of research in algorithmic game theory. Classical work on such bounds in repeated games makes the strong assumption that the subsequent rounds of the repeated games are independent beyond any influence on play from past history. This work studies such bounds in environments that themselves change due to the actions of the agents. Concretely, we consider this problem in discrete-time queuing systems, where competitive queues try to get their packets served. In this model, a queue gets to send a packet at each step to one of the servers, which will attempt to serve the oldest arriving packet, and unprocessed packets are returned to each queue. We model this as a repeated game where queues compete for the capacity of the servers, but where the state of the game evolves as the length of each queue varies. We analyze this queuing system from multiple perspectives. As a baseline measure, we first establish precise conditions on the queuing arrival rates and service capacities that ensure all packets clear efficiently under centralized coordination. We then show that if queues strategically choose servers according to independent and stationary distributions, the system remains stable provided it would be stable under coordination with arrival rates scaled up by a factor of just \(\frac{e}{e-1}\) . Finally, we extend these results to no-regret learning dynamics: if queues use learning algorithms satisfying the no-regret property to choose servers, then the requisite factor increases to 2, and both of these bounds are tight. Both of these results require new probabilistic techniques compared to the classical price of anarchy literature and show that in such settings, no-regret learning can exhibit efficiency loss due to myopia.

Fast mixing of random walks on hypergraphs (simplicial complexes) has recently led to myriad breakthroughs throughout theoretical computer science. Many important applications, however, (e.g. to LTCs, 2-2 games) rely on a more general class of underlying structures called posets, and crucially take advantage of non-simplicial structure. These works make it clear that the global expansion properties of posets depend strongly on their underlying architecture (e.g. simplicial, cubical, linear algebraic), but the overall phenomenon remains poorly understood. In this work, we quantify the advantage of different poset architectures in both a spectral and combinatorial sense, highlighting how regularity controls the spectral decay and edge-expansion of corresponding random walks. We show that the spectra of walks on expanding posets (Dikstein, Dinur, Filmus, Harsha APPROX-RANDOM 2018) concentrate in strips around a small number of approximate eigenvalues controlled by the regularity of the underlying poset. This gives a simple condition to identify poset architectures (e.g. the Grassmann) that exhibit strong (even exponential) decay of eigenvalues, versus architectures like hypergraphs whose eigenvalues decay linearly - a crucial distinction in applications to hardness of approximation and agreement testing such as the recent proof of the 2-2 Games Conjecture (Khot, Minzer, Safra FOCS 2018). We show these results lead to a tight characterization of edge-expansion on expanding posets in the 𝓁₂-regime (generalizing recent work of Bafna, Hopkins, Kaufman, and Lovett (SODA 2022)), and pay special attention to the case of the Grassmann where we show our results are tight for a natural set of sparsifications of the Grassmann graphs. We note for clarity that our results do not recover the characterization of expansion used in the proof of the 2-2 Games Conjecture which relies on 𝓁_∞ rather than 𝓁₂-structure.

We prove new results on the polarizing random walk framework introduced in recent works of Chattopadhyay et al. [Chattopadhyay et al., 2019; Eshan Chattopadhyay et al., 2019] that exploit L₁ Fourier tail bounds for classes of Boolean functions to construct pseudorandom generators (PRGs). We show that given a bound on the k-th level of the Fourier spectrum, one can construct a PRG with a seed length whose quality scales with k. This interpolates previous works, which either require Fourier bounds on all levels [Chattopadhyay et al., 2019], or have polynomial dependence on the error parameter in the seed length [Eshan Chattopadhyay et al., 2019], and thus answers an open question in [Eshan Chattopadhyay et al., 2019]. As an example, we show that for polynomial error, Fourier bounds on the first O(log n) levels is sufficient to recover the seed length in [Chattopadhyay et al., 2019], which requires bounds on the entire tail. We obtain our results by an alternate analysis of fractional PRGs using Taylor’s theorem and bounding the degree-k Lagrange remainder term using multilinearity and random restrictions. Interestingly, our analysis relies only on the level-k unsigned Fourier sum, which is potentially a much smaller quantity than the L₁ notion in previous works. By generalizing a connection established in [Chattopadhyay et al., 2020], we give a new reduction from constructing PRGs to proving correlation bounds. Finally, using these improvements we show how to obtain a PRG for 𝔽₂ polynomials with seed length close to the state-of-the-art construction due to Viola [Emanuele Viola, 2009].

In light of increasing recent attention to political polarization, understanding how polarization can arise poses an important theoretical question. While more classical models of opinion dynamics seem poorly equipped to study this phenomenon, a recent novel approach by H\ka zł a, Jin, Mossel, and Ramnarayan (HJMR) proposes a simple geometric model of opinion evolution that provably exhibits strong polarization in specialized cases. Moreover, polarization arises quite organically in their model: in each time step, each agent updates opinions according to their correlation/response with an issue drawn at random. However, their techniques do not seem to extend beyond a set of special cases they identify, which benefit from fragile symmetry or contractiveness assumptions, leaving open how general this phenomenon really is.

We consider the problem of selfish agents in discrete-time queuing systems, where competitive queues try to get their packets served. In this model, a queue gets to send a packet each step to one of the servers, which will attempt to serve the oldest arriving packet, and unprocessed packets are returned to each queue. We model this as a repeated game where queues compete for the capacity of the servers, but where the state of the game evolves as the length of each queue varies, resulting in a highly dependent random process. In classical work for learning in repeated games, the learners evaluate the outcome of their strategy in each step---in our context, this means that queues estimate their success probability at each server. Earlier work by the authors [in EC'20] shows that with no-regret learners, the system needs twice the capacity as would be required in the coordinated setting to ensure queue lengths remain stable despite the selfish behavior of the queues. In this paper, we demonstrate that this myopic way of evaluating outcomes is suboptimal: if more patient queues choose strategies that selfishly maximize their long-run success rate, stability can be ensured with just e/e-1 ~1.58 times extra capacity, strictly better than what is possible assuming the no-regret property.

In this paper, we study the connections between network structure, opinion dynamics, and an adversary's power to artificially induce disagreements. We approach these questions by extending models of opinion formation in the mathematical social sciences to represent scenarios, familiar from recent events, in which external actors have sought to destabilize communities through sophisticated information warfare tactics via fake news and bots. In many instances, the intrinsic goals of these efforts are not necessarily to shift the overall sentiment of the network towards a particular policy, but rather to induce discord. These perturbations will diffuse via opinion dynamics on the underlying network, through mechanisms that have been analyzed and abstracted through work in computer science and the social sciences. Here we investigate the properties of such attacks, considering optimal strategies both for the adversary seeking to create disagreement and for the entities tasked with defending the network from attack. By employing spectral techniques, we show that for different formulations of these types of objectives, different regimes of the spectral structure of the network will limit the adversary's capacity to sow discord; in fact, somewhat surprisingly, the entire spectrum can be relevant, rather than just the extreme eigenvectors. Via the strong connections between spectral and structural properties of graphs, we are able to qualitatively describe which networks are most vulnerable or resilient against these perturbations. We then consider the algorithmic task of a network defender to mitigate these sorts of adversarial attacks by insulating nodes heterogeneously; we show that, by considering the geometry of this problem, this optimization task can be efficiently solved via convex programming. Finally, we generalize these results to allow for two network structures, where the opinion dynamics process and the measurement of disagreement become uncoupled; for instance, this may arise when opinion dynamics are controlled by an online community via social media, while disagreement is measured along "real-world" connections. We characterize conditions on the relationship between these two graphs that will determine how much power the adversary gains when this occurs.

Bounding the price of anarchy, which quantifies the damage to social welfare due to selfish behavior of the participants, has been an important area of research in algorithmic game theory. In this paper, we study this phenomenon in the context of a game modeling queuing systems: routers compete for servers, where packets that do not get service will be resent at future rounds, resulting in a system where the number of packets at each round depends on the success of the routers in the previous rounds. We model this as an (infinitely) repeated game, where the system holds a state (number of packets held by each queue) that arises from the results of the previous rounds. We assume that routers satisfy the no-regret condition, e.g. they use learning strategies to identify the server where their packets get the best service.