Study on 2-valued dynamics on complex plane, showing some dynamics can't be group actions.
problem Whether 2-valued dynamics can be defined by the action of a 2-valued group.
method Construction of examples of dynamics that are or are not group actions.
result Some 2-valued dynamics on complex plane cannot be defined by the action of a 2-valued group.
Deep RBVFs improve continuous control in RL.
problem Challenges in finding optimal actions for continuous actions in RL.
method Introduced deep radial-basis value functions (RBVFs) for continuous control.
result RBF-DQN significantly outperforms value-function-only baselines and is competitive with actor-critic algorithms.
Study shows financial value of weak information converges in discrete vs continuous markets.
problem Analyzing financial value of weak information in discrete vs continuous markets.
method Defined minimal probability measure and financial value of weak information, then showed convergence.
result Financial value of weak information converges in discrete vs continuous markets.
New model learning objective improves continuous control tasks.
problem Challenges in solving continuous control tasks using model-based reinforcement learning.
method Derived a novel value-aware model learning objective and identified and addressed stale value estimates issue.
result Value-aware objectives can be successfully deployed in solving continuous control tasks without tuning hyper-parameters.
Revisits superhedging under proportional costs in continuous time markets.
problem Superhedging in markets with proportional transaction costs.
method Set-valued stochastic analysis, continuous trading schemes, dynamic risk measure.
result Dynamic set-valued risk measure with multi-portfolio time-consistency.
Method bounds continuous-valued treatment effects when confounding variables are hidden.
problem Inferring causal effects of continuous treatments when hidden confounders are present.
method Novel methodology to bound average and conditional average continuous-valued treatment effects.
result Method gives tighter coverage of true dose-response curve than existing methods.
Proves continuity and singular set dimension for 2D maps with Q values.
problem Interior regularity of 2D Q-valued maps. method Strong concentration-compactness theorem for equicontinuous maps.
result 2D Q-valued maps are Hölder continuous with singular set dimension ≤1. A classical result in Riemannian geometry states that the absolutely continuous curves into a (finite-dimensional) Riemannian manifold form an infinite-dimensional manifold. In the present paper this construction and related results are generalised to absolutely continuous curves with values in a strong Riemannian mani…
New approach shows continuity and compactness of martingale measures.
problem Stability of martingale optimal transport problem.
method Set-valued map theory and lower-upper hemicontinuity.
result Lower and upper hemicontinuity of the set of martingale measures.
Novel simplex-valued distribution improves on existing models.
problem Limitations of existing simplex-valued distributions like Dirichlet.
method Introducing continuous categorical distribution.
result Continuous categorical resolves limitations of Dirichlet.
Proposes a value-based method for continuous control without an actor.
problem Computational infeasibility of evaluating Q-values in continuous action spaces.
method Structurally maximizable Q-functions, actor-free approach.
result Performance and sample efficiency comparable to actor-critic methods.
Researchers develop neural networks for approximating functions in Banach spaces.
problem Approximating Banach space valued continuous functions.
method Quasi-interpolation Banach space valued neural network operators using algebraic sigmoid functions.
result Jackson type inequalities for function approximation.
Estimating causal models from observational data is a crucial task in data analysis. For continuous-valued data, Shimizu et al. have proposed a linear acyclic non-Gaussian model to understand the data generating process, and have shown that their model is identifiable when the number of data is sufficiently large. Howe…
Classifies contravariant matrix-valued valuations on polytopes without continuity assumptions.
problem Classifying contravariant matrix-valued valuations on polytopes without continuity assumptions.
method Complete classification of contravariant matrix-valued valuations on polytopes in Rn without continuity assumptions. result The only such valuation is the general Lutwak-Yang-Zhang matrix in dimension n≥4, and a new function in dimension 3. Binary encoding enables neural networks to extrapolate periodic functions.
problem Extrapolating periodic functions without prior knowledge of their form.
method Normalized Base-2 Encoding (NB2E) for continuous numerical values.
result MLPs using NB2E can successfully extrapolate diverse periodic signals.
This work takes up the challenges of utility maximization problem when the market is indivisible and the transaction costs are included. First there is a so-called solvency region given by the minimum margin requirement in the problem formulation. Then the associated utility maximization is formulated as an optimal swi…
The problem of pricing Bermudan options using Monte Carlo and a nonparametric regression is considered. We derive optimal non-asymptotic bounds for a lower biased estimate based on the suboptimal stopping rule constructed using some estimates of continuation values. These estimates may be of different nature, they may …
Unified Bayesian Optimisation for mixed variables improves performance.
problem Efficient optimisation of problems with both categorical and continuous variables.
method Derive value proposals from the Expected Improvement criterion to optimise both categorical and continuous variables under a single acquisition metric.
result Unified approach significantly outperforms existing methods across mixed-variable tasks.
Paper proves equivalence of derivatives for maps between Carnot groups.
problem Maps between Carnot groups and their derivatives.
method Elementary proof using Euclidean arguments and mean value estimates.
result Maps preserving horizontal curves are continuously Pansu differentiable.
This paper is a continuation of Ishitani and Kato (2015), in which we derived a continuous-time value function corresponding to an optimal execution problem with uncertain market impact as the limit of a discrete-time value function. Here, we investigate some properties of the derived value function. In particular, we …
The paper uses regression trees/random forests to price Bermudan options more efficiently.
problem Pricing Bermudan options with conditional expectation estimation.
method Estimates conditional expectations using regression trees or random forests instead of traditional regression methods.
result Regression trees/random forests provide better results in high dimensions.
New method for RL tasks transfer using Lipschitz continuity.
problem Knowledge transfer in RL tasks over time.
method Established Lipschitz continuity between MDPs and applied it to RL.
result Improved convergence rate and no negative transfer with high probability.
New algorithm learns value and advantage functions for continuous-time Markov processes without structural assumptions.
problem Learning value and advantage functions for continuous-time Markov processes without structural assumptions.
method Proposes Sobolev-prox fitted q-learning algorithm based on Hilbert-space positive definiteness and boundedness properties of Bellman operators. result Identifies ellipticity as a key structural property enabling reinforcement learning for Markov diffusions.
In this paper, we consider the problem of black box continuous submodular maximization where we only have access to the function values and no information about the derivatives is provided. For a monotone and continuous DR-submodular function, and subject to a bounded convex body constraint, we propose Black-box Contin…
Efficient optimisation of black-box problems that comprise both continuous and categorical inputs is important, yet poses significant challenges. We propose a new approach, Continuous and Categorical Bayesian Optimisation (CoCaBO), which combines the strengths of multi-armed bandits and Bayesian optimisation to select …
The paper improves energy decay estimates for Dir-stationary Q-valued functions and applies them to Liouville-type theorems and continuity.
problem Improving energy decay estimates for Dir-stationary Q-valued functions.
method Establishing improved decay estimates and applying them to derive Liouville-type theorems and continuity.
result Dir-stationary Q-valued functions exhibit the Lebesgue property and reside in a generalized Campanato-Morrey space.
This paper investigates methods for quantifying similarity between audio signals, specifically for the task of of cover song detection. We consider an information-theoretic approach, where we compute pairwise measures of predictability between time series. We compare discrete-valued approaches operating on quantised au…
The paper extends consistency results for sequential design strategies to vector-valued Gaussian processes.
problem Estimating excursion sets of vector-valued Gaussian processes.
method Clarifying the connection between continuous Gaussian processes and Gaussian measures in Banach spaces, extending concepts and properties from scalar-valued settings to vector-valued settings.
result Consistency results for sequential design strategies can be applied to vector-valued Gaussian processes.
Solves complex equation for specific geometric solitons.
problem Solving complex Monge-Ampère equation for specific geometric solitons.
method Aubin continuity path and continuity method.
result Initial value of the path parameter has a solution and is open to all.
New invariants detect Fano varieties' K-stability.
problem Detecting K-stability in Fano varieties.
method Introducing valuative invariants based on higher moments.
result Can detect K-stability of Fano varieties.
We study an optimal execution problem with uncertain market impact to derive a more realistic market model. We construct a discrete-time model as a value function for optimal execution. Market impact is formulated as the product of a deterministic part increasing with execution volume and a positive stochastic noise pa…
Paper tackles RL with continuous actions and unmeasured confounders.
problem Offline policy learning with continuous actions and unmeasured confounders.
method Developed a novel identification result and a minimax estimator for nonparametric policy value estimation.
result Introduced a policy-gradient-based algorithm to identify the optimal policy.
A new method for interpreting AI models using Shapley value for functional data.
problem Interpreting AI models, especially those based on functional data.
method Proposes an interpretability method based on the Shapley value for continuous games.
result Demonstrates the effectiveness of the method through experiments with simulated and real data.
We present the first PAC optimal algorithm for Bayes-Adaptive Markov Decision Processes (BAMDPs) in continuous state and action spaces, to the best of our knowledge. The BAMDP framework elegantly addresses model uncertainty by incorporating Bayesian belief updates into long-term expected return. However, computing an e…
Paper proposes a new method to select memory data for online class-incremental learning.
problem Selecting which buffered images to replay for online class-incremental learning.
method Adversarial Shapley value scoring method to preserve latent decision boundaries.
result Proposed ASER method provides competitive or improved performance compared to state-of-the-art methods.
Despite recent successes in Reinforcement Learning, value-based methods often suffer from high variance hindering performance. In this paper, we illustrate this in a continuous control setting where state of the art methods perform poorly whenever sensor noise is introduced. To overcome this issue, we introduce Recurre…
Continuity of roots of hyperbolic polynomials with smooth coefficients.
problem Continuity of the solution map for hyperbolic polynomials.
method Proving continuity of the solution map from hyperbolic polynomials of degree d with C^d coefficients to their increasingly ordered roots.
result Continuity of the solution map for hyperbolic polynomials with C^d coefficients.
In this paper we present a nonparametric method for extending functional regression methodology to the situation where more than one functional covariate is used to predict a functional response. Borrowing the idea from Kadri et al. (2010a), the method, which support mixed discrete and continuous explanatory variables,…
We study an optimal execution problem in a continuous-time market model that considers market impact. We formulate the problem as a stochastic control problem and investigate properties of the corresponding value function. We find that right-continuity at the time origin is associated with the strength of market impact…
A new approach to continuous-time universal portfolios using pathwise Itô calculus.
problem Continuous-time version of Cover's universal portfolio strategies.
method Pathwise Itô calculus approach to establish existence and properties of universal portfolio strategies.
result The universal portfolio strategy's portfolio value process is the average of all values of constant rebalanced strategies.
Develops scalable methods to assess sensitivity and uncertainty in continuous treatment effects.
problem Estimating effects of continuous-valued interventions from observational data, especially when ignorability and positivity assumptions are violated.
method Continuous treatment-effect marginal sensitivity model (CMSM), scalable algorithm, uncertainty-aware deep models.
result Derives bounds that agree with observed data and a defined level of hidden confounding.
Why is ``worthless'' fiat money generally accepted as payment for goods and services? In equilibrium theory, the value of money is generally not determined: the number of equations is one less than the number of unknowns, so only relative prices are determined. In the language of mathematics, the equations are ``homoge…
New method decomposes profits and losses continuously, avoiding discrete reporting issues.
problem Analyzing profits and losses at discrete dates ignores detailed paths.
method Constructs a large class of continuous-time decompositions using extended Itô's formula.
result Identifies a preferred decomposition from exactness, symmetry, and normalization axioms.
Study uses actor-critic method for continuous-time mean-field control with entropy regularisation.
problem Continuous-time mean-field control in reinforcement learning.
method Actor-critic approach with entropy regularisation, value function alternation, and Wasserstein space parametrisation.
result Derives exact parametrisation of actor and critic functions in linear-quadratic mean-field framework.
We present a dynamical many-body theory of money in which the value of money is a time dependent ``strategic variable'' that is chosen by the individual agents. The value of money in equilibrium is not fixed by the equations, and thus represents a continuous symmetry. The dynamics breaks this continuous symmetry by fix…
In this paper we establish the basic tools to develop the "Calculus" associated with group-valued continuously Pansu differentiable mappings. We develop the technical machinery on which all of our results rely. In particular, the linearization of addends appearing in the Baker-Campbell-Hausdorff formula is one of the m…
Introduces CHL, a new loss function for continuous similarity learning.
problem Binary similarity learning limitations.
method CHL is a novel loss function that generalizes histogram loss to continuous similarities.
result CHL solves a wider range of tasks including similarity learning, representation learning, and data visualization.
Let A be a Hölder continuous cocycle over a hyperbolic dynamical system with values in the group of diffeomorphisms of a compact manifold M. We consider the periodic data of A, i.e., the set of its return values along the periodic orbits in the base. We show that if the periodic data of A is bounded in Diff$^{\…