Denizalp Goktas

Denizalp Goktas, Gerardo Riaño-Briceño, Alif Abdullah et al.

Foundation models have transformed natural language processing and computer vision, and a rapidly growing literature on time-series foundation models (TSFMs) seeks to replicate this success in forecasting. While recent open-source models demonstrate the promise of TSFMs, the field lacks a comprehensive and community-accepted model evaluation framework. We see at least four major issues impeding progress on the development of such a framework. First, existing evaluation frameworks comprise benchmark forecasting tasks derived from often outdated datasets (e.g., M3), many of which lack clear metadata and overlap with the corpora used to pre-train TSFMs. Second, these frameworks evaluate models along a narrowly defined set of benchmark forecasting tasks, such as forecast horizon length or domain, but overlook core statistical properties such as non-stationarity and seasonality. Third, domain-specific models (e.g., XGBoost) are often compared unfairly, as existing frameworks do not enforce a systematic and consistent hyperparameter tuning convention for all models. Fourth, visualization tools for interpreting comparative performance are lacking. To address these issues, we introduce TempusBench, an open-source evaluation framework for TSFMs. TempusBench consists of 1) new datasets which are not included in existing TSFM pretraining corpora, 2) a set of novel benchmark tasks that go beyond existing ones, 3) a model evaluation pipeline with a standardized hyperparameter tuning protocol, and 4) a tensorboard-based visualization interface. We provide access to our code on GitHub: https://github.com/Smlcrm/TempusBench and maintain a live leaderboard at https://benchmark.smlcrm.com/.

Denizalp Goktas, Jiayi Zhao, Amy Greenwald

The behavior of no-regret learning algorithms is well understood in two-player min-max (i.e, zero-sum) games. In this paper, we investigate the behavior of no-regret learning in min-max games with dependent strategy sets, where the strategy of the first player constrains the behavior of the second. Such games are best understood as sequential, i.e., min-max Stackelberg, games. We consider two settings, one in which only the first player chooses their actions using a no-regret algorithm while the second player best responds, and one in which both players use no-regret algorithms. For the former case, we show that no-regret dynamics converge to a Stackelberg equilibrium. For the latter case, we introduce a new type of regret, which we call Lagrangian regret, and show that if both players minimize their Lagrangian regrets, then play converges to a Stackelberg equilibrium. We then observe that online mirror descent (OMD) dynamics in these two settings correspond respectively to a known nested (i.e., sequential) gradient descent-ascent (GDA) algorithm and a new simultaneous GDA-like algorithm, thereby establishing convergence of these algorithms to Stackelberg equilibrium. Finally, we analyze the robustness of OMD dynamics to perturbations by investigating online min-max Stackelberg games. We prove that OMD dynamics are robust for a large class of online min-max games with independent strategy sets. In the dependent case, we demonstrate the robustness of OMD dynamics experimentally by simulating them in online Fisher markets, a canonical example of a min-max Stackelberg game with dependent strategy sets.

Xan Carey, Yash Deshmukh, Aileen Huang et al.

Time-series forecasting is central to many scientific and industrial domains, such as energy systems, climate modeling, finance, and retail. While forecasting methods have evolved from classical statistical models to automated, and neural approaches, the surrounding software ecosystem remains anchored to the traditional Python numerical stack. Existing libraries rely on interpreter-driven execution and object-oriented abstractions, limiting composability, large-scale parallelism, and integration with modern differentiable and accelerator-oriented workflows. Meanwhile, today's forecasting increasingly involves large collections of heterogeneous time series data, irregular covariates, and frequent retraining, placing new demands on scalability and execution efficiency. JAX offers an alternative paradigm to traditional stateful numerical computation frameworks based on pure functions and program transformations such as just-in-time compilation and automatic vectorization, enabling end-to-end optimization across CPUs, GPUs, and TPUs. However, this modern paradigm has not yet been fully incorporated into the design of forecasting systems. We introduce Chronax, a JAX-native time-series forecasting library that rethinks forecasting abstractions around functional purity, composable transformations, and accelerator-ready execution. By representing preprocessing, modeling, and multi-horizon prediction as pure JAX functions, Chronax enables scalable multi-series forecasting, model-agnostic conformal uncertainty quantification, and seamless integration with modern machine learning and scientific computing pipelines.

Arjun Prakash, Naicheng He, Denizalp Goktas et al.

The dependency of the actor on the critic in actor-critic (AC) reinforcement learning means that AC can be characterized as a bilevel optimization (BLO) problem, also called a Stackelberg game. This characterization motivates two modifications to vanilla AC algorithms. First, the critic's update should be nested to learn a best response to the actor's policy. Second, the actor should update according to a hypergradient that takes changes in the critic's behavior into account. Computing this hypergradient involves finding an inverse Hessian vector product, a process that can be numerically unstable. We thus propose a new algorithm, Bilevel Policy Optimization with Nyström Hypergradients (BLPO), which uses nesting to account for the nested structure of BLO, and leverages the Nyström method to compute the hypergradient. Theoretically, we prove BLPO converges to (a point that satisfies the necessary conditions for) a local strong Stackelberg equilibrium in polynomial time with high probability, assuming a linear parametrization of the critic's objective. Empirically, we demonstrate that BLPO performs on par with or better than PPO on a variety of discrete and continuous control tasks.

Denizalp Goktas, Amy Greenwald, Sadie Zhao et al.

In this paper, we study inverse game theory (resp. inverse multiagent learning) in which the goal is to find parameters of a game's payoff functions for which the expected (resp. sampled) behavior is an equilibrium. We formulate these problems as generative-adversarial (i.e., min-max) optimization problems, for which we develop polynomial-time algorithms to solve, the former of which relies on an exact first-order oracle, and the latter, a stochastic one. We extend our approach to solve inverse multiagent simulacral learning in polynomial time and number of samples. In these problems, we seek a simulacrum, meaning parameters and an associated equilibrium that replicate the given observations in expectation. We find that our approach outperforms the widely-used ARIMA method in predicting prices in Spanish electricity markets based on time-series data.

Denizalp Goktas, Amy Greenwald

Min-max optimization problems (i.e., min-max games) have been attracting a great deal of attention because of their applicability to a wide range of machine learning problems. Although significant progress has been made recently, the literature to date has focused on games with independent strategy sets; little is known about solving games with dependent strategy sets, which can be characterized as min-max Stackelberg games. We introduce two first-order methods that solve a large class of convex-concave min-max Stackelberg games, and show that our methods converge in polynomial time. Min-max Stackelberg games were first studied by Wald, under the posthumous name of Wald's maximin model, a variant of which is the main paradigm used in robust optimization, which means that our methods can likewise solve many convex robust optimization problems. We observe that the computation of competitive equilibria in Fisher markets also comprises a min-max Stackelberg game. Further, we demonstrate the efficacy and efficiency of our algorithms in practice by computing competitive equilibria in Fisher markets with varying utility structures. Our experiments suggest potential ways to extend our theoretical results, by demonstrating how different smoothness properties can affect the convergence rate of our algorithms.