Related papers: Closed-form approximations in multi-asset market m…
Model Predictive Control has emerged as a popular tool for robots to generate complex motions. However, the real-time requirement has limited the use of hard constraints and large preview horizons, which are necessary to ensure safety and…
We consider the approximation of manifold-valued functions by embedding the manifold into a higher dimensional space, applying a vector-valued approximation operator and projecting the resulting vector back to the manifold. It is well known…
We present a method for constructing global analytical expressions that approximate a function over its entire range. These approximations not only mirror the original function as accurately as desired, but are purposefully created to…
We establish a quantitative approximation formula of the Lyapunov exponent of a rational function of degree more than one over an algebraically closed field of characteristic $0$ that is complete with respect to a non-trivial and possibly…
We provide performance guarantees for a variant of simulation-based policy iteration for controlling Markov decision processes that involves the use of stochastic approximation algorithms along with state-of-the-art techniques that are…
We introduce a new approximate solution technique for first-order Markov decision processes (FOMDPs). Representing the value function linearly w.r.t. a set of first-order basis functions, we compute suitable weights by casting the…
We propose a new perspective on representation learning in reinforcement learning based on geometric properties of the space of value functions. We leverage this perspective to provide formal evidence regarding the usefulness of value…
We develop a stochastic approximation-type algorithm to solve finite state/action, infinite-horizon, risk-aware Markov decision processes. Our algorithm has two loops. The inner loop computes the risk by solving a stochastic saddle-point…
There have been key advancements to building universal approximators for multi-goal collections of reinforcement learning value functions -- key elements in estimating long-term returns of states in a parameterized manner. We extend this to…
Weighted finite automata (WFA) are often used to represent probabilistic models, such as $n$-gram language models, since they are efficient for recognition tasks in time and space. The probabilistic source to be represented as a WFA,…
Starting from the Avellaneda-Stoikov framework, we consider a market maker who wants to optimally set bid/ask quotes over a finite time horizon, to maximize her expected utility. The intensities of the orders she receives depend not only on…
Existing value function approximation methods have been successfully used in many applications, but they often lack useful a priori error bounds. We propose a new approximate bilinear programming formulation of value function approximation,…
An agent's ability to leverage past experience is critical for efficiently solving new tasks. Approximate solutions for new tasks can be obtained from previously derived value functions, as demonstrated by research on transfer learning,…
Market makers continuously set bid and ask quotes for the stocks they have under consideration. Hence they face a complex optimization problem in which their return, based on the bid-ask spread they quote and the frequency at which they…
Some expansion methods have been proposed for approximately pricing options which has no exact closed formula. Benhamou et al. (2010) presents the smart expansion method that directly expands the expectation value of payoff function with…
Over the past decade, many dealers have implemented algorithmic models to automatically respond to RFQs and manage flows originating from their electronic platforms. In parallel, building on the foundational work of Ho and Stoll, and later…
This article establishes a complete approximate axiomatization for the real-closed field $\mathbb{R}$ expanded with all differentially-defined functions, including special functions such as $\sin(x), \cos(x), e^x, \dots$. Every true…
Managing a book of options on several underlying involves controlling positions of several thousands of financial assets. It is one of the most challenging financial problems involving both pricing and microstructural modeling. An options…
It was recently shown in [http://arxiv.org/abs/1207.5518] that revenue optimization can be computationally efficiently reduced to welfare optimization in all multi-dimensional Bayesian auction problems with arbitrary (possibly…
We investigate the classes of functions whose minimization diagrams can be approximated efficiently in \Re^d. We present a general framework and a data-structure that can be used to approximate the minimization diagram of such functions.…