New offline RL method handles average-reward MDPs with single-policy coverage.
problem Challenges in offline reinforcement learning due to distribution shift and non-uniform coverage.
method Develops an algorithm based on pessimistic discounted value iteration with quantile clipping.
result First fully single-policy sample complexity bound for average-reward offline RL.
Pessimistic Minimax Value Iteration finds efficient NE policies from offline data.
problem Finding an approximate Nash equilibrium in offline Markov games with non-uniform coverage.
method Pessimistic Minimax Value Iteration (PMVI) constructs pessimistic value function estimates and solves NEs.
result Established a nearly minimax optimal result for offline Markov games with function approximation.
Papers learn from data to make decisions without interacting, improving on previous methods.
problem Achieving optimal decision-making from offline data with non-linear function approximation.
method Pessimistic Nonlinear Least-Square Value Iteration (PNLSVI) with three innovative components.
result Achieves minimax optimal instance-dependent regret for non-linear function approximation.
Study tight offline learning bounds for linear MDPs using variance information.
problem Understanding statistical limits with linear function representations in offline reinforcement learning.
method Variance-aware pessimistic value iteration (VAPVI) that reweights Bellman residuals based on estimated variances.
result Improved offline learning bounds expressed in terms of system quantities.
Pessimistic Q-learning improves sample efficiency in offline reinforcement learning.
problem Insufficient coverage and sample scarcity in offline reinforcement learning datasets.
method Pessimistic Q-learning algorithm for offline reinforcement learning, focusing on variance reduction.
result Near-optimal sample complexity achieved with the proposed algorithm.
New algorithm reduces reinforcement learning regret to sqrt(T) without strong dynamics assumptions.
problem Infinite-horizon average-reward reinforcement learning with linear MDPs.
method Approximate by discounted-reward MDPs and apply optimistic value iteration.
result Achieves O(sqrt(T)) regret with polynomial complexity.
Study optimal portfolio strategies with time-varying discount rates.
problem Optimizing portfolio decisions with a non-constant discount rate.
method Introduced subgame perfect strategies to handle time inconsistency, using fixed point iteration to find the utility-weighted discount rate.
result Subgame perfect strategies are equivalent to optimal strategies under certain utility function assumptions.
Policy gradient methods with aggregated states can achieve better performance than approximate policy iteration.
problem Approximation errors in policy and value function approximations.
method State-aggregated representations and policy gradient methods.
result Policy gradient methods can achieve a per-period regret bounded by ε, while approximate policy iteration and value iteration have a higher regret.
A new algorithm for offline RL with trajectory-wise reward reduces bias and variance errors.
problem Offline RL with trajectory-wise reward incurs large bias and variance errors.
method PARTED algorithm that decomposes trajectory return into proxy rewards and performs pessimistic value iteration.
result PARTED achieves provably efficient suboptimality bounds in general MDPs with trajectory-wise reward.
Faster algorithms for solving multichain MDPs under average-reward criterion.
problem Navigating towards the best connected component in multichain MDPs.
method Developed algorithms to better solve the navigational subproblem, achieving faster convergence rates.
result Improved rates of convergence and sharper complexity measures for multichain MDPs.
We demonstrate a limitation of discounted expected utility, a standard approach for representing the preference to risk when future cost is discounted. Specifically, we provide an example of the preference of a decision maker that appears to be rational but cannot be represented with any discounted expected utility. A …
Value iteration is a fixed point iteration technique utilized to obtain the optimal value function and policy in a discounted reward Markov Decision Process (MDP). Here, a contraction operator is constructed and applied repeatedly to arrive at the optimal solution. Value iteration is a first order method and therefore …
New algorithms accelerate value function convergence in MDPs.
problem Accelerating convergence of value functions in Markov Decision Processes (MDPs).
method Operator Splitting Value Iteration (OS-VI) and OS-Dyna.
result Achieves much faster convergence rate with accurate models.
We study an infinite-horizon discrete-time optimal stopping problem under non-exponential discounting. A new method, which we call the iterative approach, is developed to find subgame perfect Nash equilibria. When the discount function induces decreasing impatience, we establish the existence of an equilibrium through …
New method for optimistic planning in MDPs using regularization.
problem Optimistic planning in infinite-horizon discounted MDPs.
method Regularized dynamic programming for approximate value iteration.
result Achieves near-optimal statistical guarantees in learning policies.
Study risk-sensitive RL in offline settings, improving efficiency and accuracy.
problem Efficiently derive near-optimal policies for risk-sensitive RL using offline data.
method Introduced two provably sample-efficient algorithms for risk-sensitive offline RL in linear MDPs.
result First provably efficient risk-sensitive offline RL algorithms.
Proposes Optimistic Pessimistically Initialised Q-Learning (OPIQ) for better exploration in RL.
problem Pessimistic initialisation of Q-values in deep RL leads to poor exploration performance.
method Augments pessimistically initialised Q-values with count-based bonuses to ensure optimism.
result OPIQ outperforms non-optimistic DQN variants in hard exploration tasks.
Pessimistic model-based algorithm finds Nash equilibria in zero-sum Markov games from offline data.
problem Learning Nash equilibria in two-player zero-sum Markov games from limited data.
method Pessimistic model-based algorithm with Bernstein-style lower confidence bounds (VI-LCB-Game).
result Proves sample complexity no larger than C c l i p p e d ⋆ S ( A + B ) ( 1 − γ ) 3 ε 2 \frac{C_{\mathsf{clipped}}^\star S(A+B)}{(1-γ)^3 \varepsilon^2} ( 1 − γ ) 3 ε 2 C clipped ⋆ S ( A + B ) , achieving minimax optimality. New algorithm identifies near-optimal policies in adversarial distributed RL settings.
problem Adversarial agents in distributed RL settings that can collude and report arbitrary data.
method Weighted-Clique algorithm for robust mean estimation from batches, combined with novel distributed algorithms.
result Achieves superior robustness guarantees and near-optimal sample complexities in both offline and online settings.
Paper tackles time inconsistency in portfolio management with stochastic volatility and power utility.
problem Time inconsistency in portfolio management with stochastic volatility and power utility.
method Extended Hamilton Jacobi Bellman (HJB) equation, fixed point iteration, and linear parabolic PDE.
result Subgame perfect strategies are characterized and solved through numerical experiments.
Paper tackles robust decision-making from multiple sites with shared structure.
problem Learning robust sequential decisions from heterogeneous multi-site datasets.
method Group-Robust MDPs with d-rectangular uncertainty sets, feature-wise worst-case aggregation, and cluster-level pooling.
result Proves suboptimality bound for robust planning policy under robust partial coverage assumption.
Pessimistic RL algorithm improves offline RL performance.
problem Insufficient dataset coverage in offline RL.
method Proposes a pessimistic variant of value iteration (PEVI) with a penalty function.
result Establishes upper bound on suboptimality for general MDPs, matching lower bound.
This paper is concerned with offline reinforcement learning (RL), which learns using pre-collected data without further exploration. Effective offline RL would be able to accommodate distribution shift and limited data coverage. However, prior algorithms or analyses either suffer from suboptimal sample complexities or …
Pessimistic estimator improves multi-objective policy optimization.
problem Optimizing multi-objective policies from existing data.
method Pessimistic estimator based on inverse propensity scores (IPS).
result Pessimistic estimator outperforms naive IPS estimator in theory and experiments.
Softmax PG methods can take extremely long to converge, even with exact gradients.
problem Softmax policy gradient methods can take an impractically long time to converge in reinforcement learning.
method Softmax policy gradient methods with exact gradient computation.
result Softmax PG methods can take exponential number of iterations to converge, even with optimal initialization.
Study risk-sensitive reinforcement learning with entropic risk measures and generative models.
problem Risk-sensitive reinforcement learning in discounted MDPs with recursive entropic risk measures.
method Introduced Model-Based ERM Q Q Q -Value Iteration (MB-RS-QVI) and derived PAC bounds on sample complexity for value and policy learning. result PAC bounds show exponential dependence on ∣ β ∣ / ( 1 − γ ) |β|/(1-γ) ∣ β ∣/ ( 1 − γ ) , with tight bounds in S S S and A A A . In a discounted reward Markov Decision Process (MDP), the objective is to find the optimal value function, i.e., the value function corresponding to an optimal policy. This problem reduces to solving a functional equation known as the Bellman equation and a fixed point iteration scheme known as the value iteration is u…
Reinforcement learning (RL) typically defines a discount factor as part of the Markov Decision Process. The discount factor values future rewards by an exponential scheme that leads to theoretical convergence guarantees of the Bellman equation. However, evidence from psychology, economics and neuroscience suggests that…
Paper introduces non-linear discounting models for default compensation and climate valuation.
problem Valuation of non-replicable value and damage under default risk.
method Develops two models: one for risk-neutralising discounting and another for survival probability dependent discounting.
result Non-decaying discount factors (negative discount rates) are possible under certain scenarios.
Proposes a new framework for discount models.
problem Arbitrage-free dynamic framework for discount models.
method Derives general consistency conditions for factor models.
result Alternative to Heath--Jarrow--Morton framework for forward rates.
We consider the problem of learning the optimal action-value function in the discounted-reward Markov decision processes (MDPs). We prove a new PAC bound on the sample-complexity of model-based value iteration algorithm in the presence of the generative model, which indicates that for an MDP with N state-action pairs a…
Paper develops a discounted algorithm for online convex optimization that adapts to unknown discount factors.
problem Developing an algorithm that can adapt to an unknown discount factor in online convex optimization.
method Smoothed Online Gradient Descent (SOGD) with Discounted-Normal-Predictor (DNP).
result Achieves a uniform O ( log T / 1 − λ ) O(\sqrt{\log T/1-λ}) O ( log T /1 − λ ) discounted regret across a continuous interval of discount factors. Paper tackles RLHF with DCPPO method, proving near-optimal suboptimality.
problem Challenges in offline RLHF with limited human feedback and bounded rationality.
method DCPPO method involving three stages: MLE, reward function recovery, and pessimistic value iteration.
result DCPPO's suboptimality almost matches classical pessimistic offline RL in terms of distribution shift and dimension.
New research shows exponential lower bounds for planning in MDPs with linearly-realizable optimal action-value functions.
problem Determining the minimum number of queries needed for sound planners in MDPs with linear function approximation.
method Analyzing fixed-horizon and discounted MDPs with a generative model, showing lower bounds on the number of queries required.
result Sound planners need at least exponential number of queries in both fixed-horizon and discounted settings.
A new estimator for state values in reinforcement learning reduces complexity and improves convergence.
problem Estimating state values in reinforcement learning with Markov reward processes.
method Loop estimator exploiting regenerative structure of Markov reward processes.
result Instance-dependent convergence rate of O ~ ( τ s / T ) \widetilde{O}\left(\sqrt{τ_s/T}\right) O ( τ s / T ) for estimating state values. A new method learns robust policies from offline data with latent structures.
problem Conservative policies under unrealistic dynamics shifts.
method d-RRMDP framework with f f f -divergence regularization and R2PVI algorithm. result R2PVI learns robust policies with superior computational efficiency.
Entropy-regularized NPG methods converge linearly in discounted MDPs.
problem Theoretical limitations of NPG methods in reinforcement learning.
method Entropy regularization in conjunction with NPG methods for discounted MDPs.
result Entropy-regularized NPG methods converge linearly in discounted MDPs.
Accelerates TD learning for long-horizon reinforcement learning problems.
problem Slow convergence of conventional TD learning in long-horizon tasks.
method Introduces PID Accelerated Temporal Difference (PID TD) learning algorithms.
result Accelerates convergence of TD learning compared to conventional methods.
New RL algorithms improve performance using multi-step greedy policies.
problem Improving model-free reinforcement learning performance.
method Developed multi-step greedy κ κ κ -Policy Iteration and κ κ κ -Value Iteration algorithms for model-free RL. result Multi-step greedy algorithms outperform DQN and TRPO on various benchmark tasks.
Proves lower discount rates are needed for future losses.
problem Determining appropriate discount rates for future losses.
method Analyzes climate change and discount rates debate.
result Risk requires a lower, not higher, discount rate.
Improved algorithm for optimal stopping problems reduces runtime.
problem Optimal stopping problems with infinite time horizon and random discounting.
method Flexible forward improvement iteration with a variable look-ahead distance.
result The new algorithm converges and can significantly reduce runtime.
Intertemporal decision making involves choices among options whose effects occur at different moments. These choices are influenced not only by the effect of rewards value perception at different moments, but also by the time perception effect. One of the main difficulties that affect standard experiments involving int…
In this paper, we analyze the diversity of term structure functions (e.g., yield curves, swap curves, credit curves) constructed in a process which complies with some admissible properties: arbitrage-freeness, ability to fit market quotes and a certain degree of smooth- ness. When present values of building instruments…
Framework for transferring discount curve estimates across fixed-income product classes.
problem Challenges in estimating discount curves from sparse or noisy data.
method Proposes a vector-valued kernel ridge regression (KR) framework with economic regularization.
result Transfer learning tightens confidence intervals and improves extrapolation performance.
AAPI improves regret bound for undiscounted continuing learning in uniformly ergodic MDPs.
problem Improving regret bounds for undiscounted continuing learning in uniformly ergodic MDPs.
method Adaptive approximate policy iteration (AAPI) with online learning techniques and data-dependent adaptive learning rate.
result AAPI achieves a i l d e O ( T 2 / 3 ) ilde{O}(T^{2/3}) i l d e O ( T 2/3 ) regret bound, improving over the best existing bound of i l d e O ( T 3 / 4 ) ilde{O}(T^{3/4}) i l d e O ( T 3/4 ) . We study the online estimation of the optimal policy of a Markov decision process (MDP). We propose a class of Stochastic Primal-Dual (SPD) methods which exploit the inherent minimax duality of Bellman equations. The SPD methods update a few coordinates of the value and policy estimates as a new state transition is obs…
In classical Q-learning, the objective is to maximize the sum of discounted rewards through iteratively using the Bellman equation as an update, in an attempt to estimate the action value function of the optimal policy. Conventionally, the loss function is defined as the temporal difference between the action value and…
Revises derivative pricing post financial crisis by defining a discount rate.
problem Derivative pricing became complex with XVA adjustments.
method Developed a binomial tree model for pricing with counterparty and funding risks.
result Coherent XVAs naturally result from decomposing the discount rate.