81,146 research outputs found
The target discounted-sum problem
The target discounted-sum problem is the following: Given a rational discount factor 0 < λ < 1 and three rational values a, b, and t, does there exist a finite or an infinite sequence w Δ(a, b)â or w Δ(a, b)w, such that ÎŁ|w| i=0 w(i)λi equals t? The problem turns out to relate to many fields of mathematics and computer science, and its decidability question is surprisingly hard to solve. We solve the finite version of the problem, and show the hardness of the infinite version, linking it to various areas and open problems in mathematics and computer science: ÎČ-expansions, discounted-sum automata, piecewise affine maps, and generalizations of the Cantor set. We provide some partial results to the infinite version, among which are solutions to its restriction to eventually-periodic sequences and to the cases that λ λ 1/2 or λ = 1/n, for every n Δ N. We use our results for solving some open problems on discounted-sum automata, among which are the exact-value problem for nondeterministic automata over finite words and the universality and inclusion problems for functional automata
The Adversarial Stackelberg Value in Quantitative Games
In this paper, we study the notion of adversarial Stackelberg value for two-player non-zero sum games played on bi-weighted graphs with the mean-payoff and the discounted sum functions. The adversarial Stackelberg value of Player 0 is the largest value that Player 0 can obtain when announcing her strategy to Player 1 which in turn responds with any of his best response. For the mean-payoff function, we show that the adversarial Stackelberg value is not always achievable but ?-optimal strategies exist. We show how to compute this value and prove that the associated threshold problem is in NP. For the discounted sum payoff function, we draw a link with the target discounted sum problem which explains why the problem is difficult to solve for this payoff function. We also provide solutions to related gap problems
The Adversarial Stackelberg Value in Quantitative Games
In this paper, we study the notion of adversarial Stackelberg value for
two-player non-zero sum games played on bi-weighted graphs with the mean-payoff
and the discounted sum functions. The adversarial Stackelberg value of Player 0
is the largest value that Player 0 can obtain when announcing her strategy to
Player 1 which in turn responds with any of his best response. For the
mean-payoff function, we show that the adversarial Stackelberg value is not
always achievable but epsilon-optimal strategies exist. We show how to compute
this value and prove that the associated threshold problem is in NP. For the
discounted sum payoff function, we draw a link with the target discounted sum
problem which explains why the problem is difficult to solve for this payoff
function. We also provide solutions to related gap problems.Comment: long version of an ICALP'20 pape
IST Austria Technical Report
DEC-POMDPs extend POMDPs to a multi-agent setting, where several agents operate in an uncertain environment independently to achieve a joint objective. DEC-POMDPs have been studied with finite-horizon and infinite-horizon discounted-sum objectives, and there exist solvers both for exact and approximate solutions. In this work we consider Goal-DEC-POMDPs, where given a set of target states, the objective is to ensure that the target set is reached with minimal cost. We consider the indefinite-horizon (infinite-horizon with either discounted-sum, or undiscounted-sum, where absorbing goal states have zero-cost) problem. We present a new method to solve the problem that extends methods for finite-horizon DEC- POMDPs and the RTDP-Bel approach for POMDPs. We present experimental results on several examples, and show our approach presents promising results
IST Austria Technical Report
The target discounted-sum problem is the following: Given a rational discount factor 0 < λ < 1 and three rational values a, b, and t, does there exist a finite or an infinite sequence w Δ(a, b)â or w Δ(a, b)w, such that ÎŁ|w| i=0 w(i)λi equals t? The problem turns out to relate to many fields of mathematics and computer science, and its decidability question is surprisingly hard to solve. We solve the finite version of the problem, and show the hardness of the infinite version, linking it to various areas and open problems in mathematics and computer science: ÎČ-expansions, discounted-sum automata, piecewise affine maps, and generalizations of the Cantor set. We provide some partial results to the infinite version, among which are solutions to its restriction to eventually-periodic sequences and to the cases that λ λ 1/2 or λ = 1/n, for every n Δ N. We use our results for solving some open problems on discounted-sum automata, among which are the exact-value problem for nondeterministic automata over finite words and the universality and inclusion problems for functional automata
How forward-looking is the Fed? Direct estimates from a âCalvo-typeâ rule
We estimate an alternative type of monetary policy rule, termed Calvo rule, according to which the central bank is assumed to target a discounted infinite sum of future expected inflation. Compared to conventional inflation forecast-based rules, which are typically of the Taylor-type with discrete forward looking horizons, this class of rule is less prone to the problem of indeterminacy. Parameter estimates obtained from GMM estimation provide support for Calvo-type rules, suggesting that the Federal Reserve targeted a mean forward horizon of between 4 and 8 quarters.Calvo-type interest rules, Inflation Forecast Based rules, GMM, indeterminacy.
How forward-looking is the Fed? Direct estimates from a `Calvo-type' rule
We estimate an alternative type of monetary policy rule, termed Calvo rule, according to which the central bank is assumed to target a discounted in?nite sum of future expected in?ation. Compared to conventional in?ation forecast-based rules, which are typically of the Taylor-type with discrete forward looking horizons, this class of rule is less prone to the problem of indeterminacy. Parameter estimates obtained from GMM estimation provide support for Calvo-type rules, suggesting that the Federal Reserve targeted a mean forward horizon of between 4 and 8 quarters.Calvo-type interest rules; In?ation Forecast Based rules; GMM; Indeterminacy.
Percentile Queries in Multi-Dimensional Markov Decision Processes
Markov decision processes (MDPs) with multi-dimensional weights are useful to
analyze systems with multiple objectives that may be conflicting and require
the analysis of trade-offs. We study the complexity of percentile queries in
such MDPs and give algorithms to synthesize strategies that enforce such
constraints. Given a multi-dimensional weighted MDP and a quantitative payoff
function , thresholds (one per dimension), and probability thresholds
, we show how to compute a single strategy to enforce that for all
dimensions , the probability of outcomes satisfying is at least . We consider classical quantitative payoffs from
the literature (sup, inf, lim sup, lim inf, mean-payoff, truncated sum,
discounted sum). Our work extends to the quantitative case the multi-objective
model checking problem studied by Etessami et al. in unweighted MDPs.Comment: Extended version of CAV 2015 pape
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