A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
New approach for adaptive conformal inference using Blackwell's theory.
Financial markets are often driven by latent factors which traders cannot observe. Here, we address an algorithmic trading problem with collections of heterogeneous agents who aim to perform optimal execution or statistical arbitrage, where all agents filter the latent states of the world, and their trading actions hav…
Even when confronted with the same data, agents often disagree on a model of the real-world. Here, we address the question of how interacting heterogenous agents, who disagree on what model the real-world follows, optimize their trading actions. The market has latent factors that drive prices, and agents account for th…
In the standard setting of approachability there are two players and a target set. The players play repeatedly a known vector-valued game where the first player wants to have the average vector-valued payoff converge to the target set which the other player tries to exclude it from this set. We revisit this setting in …
Abstract: Generalizes multisymplectic forms to vector-valued versions.
Boosting framework for vector-valued prediction with geometric stability.
Study confirms learning rates for vector-valued spectral algorithms, proving consistency.
The paper extends consistency results for sequential design strategies to vector-valued Gaussian processes.
We describe an approximate dynamic programming (ADP) approach to compute approximations of the optimal strategies and of the minimal losses that can be guaranteed in discounted repeated games with vector-valued losses. Such games prominently arise in the analysis of regret in repeated decision-making in adversarial env…
Paper analyzes error bounds for learning with vector-valued RF, improving existing analyses.
New method finds all Nash equilibria via vector optimization.
We prove a general duality result for multi-stage portfolio optimization problems in markets with proportional transaction costs. The financial market is described by Kabanov's model of foreign exchange markets over a finite probability space and finite-horizon discrete time steps. This framework allows us to compare v…
Develops vector-valued RKBS for neural networks and operators.
In this expository paper we illustrate the generality of game theoretic probability protocols of Shafer and Vovk (2001) in finite-horizon discrete games. By restricting ourselves to finite-horizon discrete games, we can explicitly describe how discrete distributions with finite support and the discrete pricing formulas…
We examine the relationship between nonabelian Hodge theory for Riemann surfaces and the theory of vector valued modular forms. In particular, we explain how one might use this relationship to prove a conjectural three-term inequality on the weights of free bases of vector valued modular forms associated to complex, fi…
DORIS algorithm achieves no-regret learning in Markov games with adversarial opponents.
The paper simplifies multi-agent RL dynamics in finite-state Markov games using homogenization.
In this paper, we consider multi-agent learning via online gradient descent in a class of games called -cocoercive games, a fairly broad class of games that admits many Nash equilibria and that properly includes unconstrained strongly monotone games. We characterize the finite-time last-iterate convergence rate for …
We discuss sharp Sobolev inequalities for vector valued maps.
Partial-monitoring games constitute a mathematical framework for sequential decision making problems with imperfect feedback: The learner repeatedly chooses an action, opponent responds with an outcome, and then the learner suffers a loss and receives a feedback signal, both of which are fixed functions of the action a…
A new method uses Mean Field Games to optimize mixture models of Bernoulli and categorical distributions.
Motivated by multi-task machine learning with Banach spaces, we propose the notion of vector-valued reproducing kernel Banach spaces (RKBS). Basic properties of the spaces and the associated reproducing kernels are investigated. We also present feature map constructions and several concrete examples of vector-valued RK…
Expands MFGs to handle real-world asymmetric multi-agent games efficiently.
Optimal rates for vector-valued regression on various norms.
SL(n) covariant valuations on Orlicz spaces are represented and characterized.
Study on liquidation games with market drop-out, proving unique equilibria.
We discuss a natural game of competition and solve the corresponding mean field game with \emph{common noise} when agents' rewards are \emph{rank dependent}. We use this solution to provide an approximate Nash equilibrium for the finite player game and obtain the rate of convergence.
The space of vector-valued forms on any manifold is a graded Lie algebra with respect to the Frolicher-Nijenhuis bracket. In this paper we consider multiplicative vector-valued forms on Lie groupoids and show that they naturally form a graded Lie subalgebra. Along the way, we discuss various examples and different char…
Vector-valued learning, where the output space admits a vector-valued structure, is an important problem that covers a broad family of important domains, e.g. multi-task learning and transfer learning. Using local Rademacher complexity and unlabeled data, we derive novel semi-supervised excess risk bounds for general v…
The paper shows vector-valued risk measures ignore dependence structures.
The existence of stationary Markov perfect equilibria in stochastic games is shown under a general condition called "(decomposable) coarser transition kernels". This result covers various earlier existence results on correlated equilibria, noisy stochastic games, stochastic games with finite actions and state-independe…
We describe the set of possible vector valued side lengths of n-gons in thick Euclidean buildings of rank 2. This set is determined by a finite set of homogeneous linear inequalities, which we call the generalized triangle inequalities. These inequalities are given in terms of the combinatorics of the spherical Coxeter…
The paper proposes methods to find a shared active subspace for multivariate vector-valued functions.
New algorithms optimize multiple tasks with shared similarities, reducing regret.
Optimal transport for vector Gaussian mixtures improves efficiency and structure preservation.
We present a framework to derive risk bounds for vector-valued learning with a broad class of feature maps and loss functions. Multi-task learning and one-vs-all multi-category learning are treated as examples. We discuss in detail vector-valued functions with one hidden layer, and demonstrate that the conditions under…
Novel approach to Nash equilibrium in mean-field stochastic games with operator resolvents.
Game theory models how agents trade in a risky asset considering price impact and a common signal.
Study on convergence of Langevin dynamics for zero-sum games in probability distributions.
Study best-response learning dynamics in zero-sum polymatrix games under full and minimal information settings.
Study improves self-normalized bounds for vector-valued processes beyond sub-Gaussianity.
This paper uses recent results on continuous-time finite-horizon optimal switching problems with negative switching costs to prove the existence of a saddle point in an optimal stopping (Dynkin) game. Sufficient conditions for the game's value to be continuous with respect to the time horizon are obtained using recent …
Study optimal investment strategies for competitive agents using Mean Field Games.
Geometrically convex return risk measures on AM-algebras
A quantum financial approach to finite games of strategy is addressed, with an extension of Nash's theorem to the quantum financial setting, allowing for an entanglement of games of strategy with two-period financial allocation problems that are expressed in terms of: the consumption plans' optimization problem in pure…
We approximate derivatives of functions on manifolds by embedding them and applying vector-valued operators.
FGNNs improve game-playing AI by exploiting symmetries.
Paper introduces vector-valued variation spaces for multi-output neural networks.