Ronald Howard. Dynamic Programming and Markov Processes. MIT Press, Cambridge, MA, 1960. Home/Search Document Not in Database Summary Related Articles Check |
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Markov Decision Processes With Fuzzy Rewards - Masami Kurano Masami (Correct)
....considered. Keywords: Multi dimensional fuzzy reward model, Markov decision process, Pareto optimal, fuzzy optimality equation. AMS 1991 subject classification. Primary: 90c40; Secondary: 90c39. 1. Introduction In mathematical modeling in terms of Markov decision processes (MDPs, in short, cf. [2, 6, 12, 15]) it often occurs that the information on the reward function includes imprecision or ambiguity. As an example, the reward earned in a day is about 700 dollars or closed to 800 dollars. On the other hand, multi criteria decision making is typically involving flexible requirements for the ....
Howard, R., Dynamic Programming and Markov processes, (1960), MIT Press, Cambridge MA.
Collision Resolution Algorithms for a Time-Constrained.. - Panwar, Towsley, Armoni (1993) (3 citations) (Correct)
....not be determined. We develop a CRA that exhibits thc first come, first served property, since this tends to minimize the number of packets lost [3] This CRA ensures that packets are transmitted in order of generation. To compute the performance of the CRA s we use the value iteration method [8] because it is a way of determining the optimal CRA within a class of CRA s [2] This method is briefly summarized next. Consider a finite state, discrete time, ergodie Markov chain. After each transition, the system is in one of N states i, i 1, 2, N. For each state i, an action k = 1, 2, ....
R. Howard, Dynamic Programming and Markov Processes. Cambridge, MA: MIT Press, 1960.
Minimizing the Average Cost of Paging and Registration: A.. - Rose (1995) (37 citations) (Correct)
....in terms of decision theory. In particular, one may assume the mobile terminal knows its location as well as the cost to be incurred by a paging event at time t. In as much 13 as this information characterizes the state of the system, optimal decision methods such as Markovian Decision Theory [18, 19] can be brought to bear. Furthermore, this problem might be generalized to include whatever state information is available in a practical sense such as time of day, system geography or anything else easily obtainable. Methods which use both location and time information are currently under study ....
R.A. Howard. Dynamic Programming and Markov Processes. M.I.T. Press, 1960.
Learning and Planning in Structured Worlds - Dearden (Correct)
....in this thesis can potentially be applied if we do, but there are a number of additional sources of complexity in these models, so we will restrict ourselves to the completely observable case. One common approach to modeling domains with these characteristics is to use a Markov decision process [7, 57, 58]. Markov decision processes are a very gen eral formulation of decision making problems involving various types of uncertainty and have all the desirable properties we have mentioned above. They have been extensively studied in the field of Operations Research and there is an extensive ....
....If Xt is a random variable denoting the state of the system at time t, then the value of following policy r with the world initially in state s can be written as: N vv(s) lim [ N t 1 where the expectation is over states visited while following policy r starting at state . Howard [57] has derived a more useful expression, at least from the point of view of computation, for the value of policy r. Howard s formula, which is the basis 21 Table 2.2: Two policies for the example MDP of Figure 2.1. The second is an optimal policy for this MDP. Policy i Optimal Policy State Action ....
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Ronald A. Howard. Dynamic Programming and Markov Processes. MIT Press, Cambridge, 1960. 227
Generalization over Environments in Reinforcement Learning - Matt, Regensburger (2003) (Correct)
....How do good learning environments look like 2 Preliminaries We propose the following notation for reinforcement learning models, which allows us to treat several environments and reinforcement func tions. The main difference to the standard defi nition of a Markov decision process, see Howard [3] or White [8] is, that we separate the rein forcement function from the environment. An environment is given by A finite set S of states. A family A = A(s) e of finite sets of actions. The set A(s) is interpreted as the set of all allowed actions in state s. A family of probabilities P ....
Howard, R. A.: Dynamic Programming and Markov Processes. MIT Press. Cambridge, MA (1960)
Dynamic Power Management of Complex Systems Using Generalized .. - Qiu, Wu, Pedram (2000) (12 citations) (Correct)
....modeswitching policies for the SPs) under given performance (delay) constraints. The paper is organized as follows. Sections II introduces the system modeling based on GSPN. Sections III and IV present experimental results and conclusions. Please refer to [22] 23] for background on the GSPN and [17] for background on the continuous time Markov decision process. II. System modeling using GSPN First, we give the definition of a GSPN with cost and a controllable GSPN with cost. Definition: A GSPN with cost is a GSPN model with the addition of two types of cost: impulse cost associate with ....
R.A.Howard, Dynamic Programming and Markov Processes, Wiley, New York, 1960
Piecewise Linear Value Function Approximation for Factored MDPs - Poupart, Boutilier (2002) (4 citations) (Correct)
....; V is thus a fixed point of . We denote by B the backup operator for the policy that applies action a at each state. Our aim is to find a policy # # that maximizes value at each state. The optimal VF, denoted V # , is unique and is the fixed point of the following Bellman backup operator [11] : V # (s) max a#A R(s, a) # # Pr(s, a, t) V # (t) 2) A number of algorithms exist to construct the optimal VF, including dynamic programming algorithms such as value and policy iteration. We focus here on a simple linear program (LP) whose solution is V # : Min: # s V (s) Subj. to: ....
R. A. Howard. Dynamic Programming and Markov Processes. MIT Press, Cambridge, 1960.
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....assignments of robots to frontier cells. 2. 1 Costs To determine the cost of reaching the current frontier cells, we compute the optimal path from the current position of the robot to all frontier cells based on a deterministic variant of value iteration, a popular dynamic programming algorithm [5, 27]. In our approach, the cost for traversing a grid cell hx; yi is proportional to its occupancy value P (occ xy ) The minimum cost path is computed using the following two steps. 1. Initialization. The grid cell that contains the robot location is initialized with 0, all others with 1: V x;y ....
R.A. Howard. Dynamic Programming and Markov Processes. MIT Press and Wiley, 1960.
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....q(x) and the same collection of busy servers J 1 (y) J 1 (x) 5. AN ALGORITHM The previous theorem describes only qualitative properties of the optimal policies. For the optimal threshold level calculation, an algorithm can be proposed. This algorithm is based on the Howard s iteration approach ([4]) and takes into account some specific properties of the problem. The algorithm consists of two general steps: Policy Evaluation, and Policy Improvement. To transform multidimensional massifs into a one dimensional one, the following numeration of the states is used, where numbers are denoted by ....
R.A. Howard, Dynamic programming and Markov processes (Wiley, 1960). ############## #######
Reinforcement Learning Using Neural Networks, with Applications.. - Coulom (2002) (Correct)
....It also converges when # = 1 and all values are well defined. Algorithm 1.2 Policy Evaluation V i (x) r #V i 1 end for until V has converged 1.1.5 Policy Iteration Policy Iteration is another very important approach to dynamic programming. It is attributed to Howard [31], and consists in using the policyevaluation algorithm defined previously to obtain successive improved policies. Algorithm 1.3 shows the details of this algorithm. It is rather easy to prove that, for each x, V i (x) is bounded and monotonic, which proves that this algorithm converges when # 1 ....
Ronald A. Howard. Dynamic Programming and Markov Processes. MIT Press, Cambridge, MA, 1960. 41
Generalization over Environments in Reinforcement Learning - Matt, Regensburger (2002) (Correct)
....propose the following notation for reinforcement learning models, which al lows us to treat several environments and reinforcement functions. The main partially supported by the Austrian Science Fund (FWF) Project Y 123 INF. difference to the standard definition of a Markov decision process, [3], is that we separate the reinforcement function from the environment. An environment is given by A finite set of states. A family A (A(s) se of finite sets of actions. The set A(s) is interpreted as the set of all allowed actions in state s. A family of probabilities P P( I ....
Howard, R. A.: Dynamic Programming and Markov Processes. MIT Press. Cam- bridge, MA (1960)
Non-approximability of Decentralized Control - Rabinovich, Campus, Ram, Goldman (2002) (Correct)
....reduce MIPs to Dec POMDPs. The reduction proves our nonapproximability results, i.e. finding solutions for Decentralized POMDPs that come closer than some constant to the best possible value, is NEXP hard. 2 Markov Decision Processes Markov Decision Processes (MDPs) and their related problems [2, 10, 18] are very popular mathematical models, that capture the stochastic dynamics of a system over time. The existence of an external control (the signals) in MDPs makes the model an obvious candidate for the description of agent environment interactions. In this paper, we limit our attention to a ....
Ronald A. Howard. Dynamic programming and Markov processes. MIT Press, Cambridge, MA, 1960.
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....is a map ping from states to actions. We denote by (s) the action that policy prescribes in state s. The objective is to nd a policy that maximizes P 1 t=0 E(r t j ) where r t is the payo at time t, and 2 [0; 1) is a discount factor. There exists a deterministic optimal [12]. The Q function for this policy, Q , is de ned by the set of equations Q (s; a) R(s; a) s 0 2S T (s; a; s ) max a 0 2A Q ) At any state s, the optimal policy chooses arg max a Q (s; a) 10] Reinforcement learning (RL) 7] can be viewed as a sampling method for ....
R.A.Howard. Dynamic programming and Markov processes. MIT Press, 1960.
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