diff --git a/Data/Teams/Examples/DecMdp.hs b/Data/Teams/Examples/DecMdp.hs new file mode 100644 --- /dev/null +++ b/Data/Teams/Examples/DecMdp.hs @@ -0,0 +1,25 @@ +-- | Decentralized MDP +-- Based on an email exchange with Ashutosh Nayyar + +module Data.Teams.Examples.DecMdp where +import Data.Teams.Structure + +x = mkNonReward "x" +u1 = mkNonReward "u1" +u2 = mkNonReward "u2" +r = mkReward "r" + +f = mkDynamics "f" +g1 = mkControl "g1" +g2 = mkControl "g2" +d = mkDynamics "d" + +dynamics t = f(t).$.(x(t) .|. if t == 1 then [] else [x(t-1), u1(t-1), u2(t-1)]) + ++ g1(t).$.(u1(t) .|. map x[1..t] ++ map u1[1..t-1]) + ++ g2(t).$.(u2(t) .|. map x[1..t] ++ map u2[1..t-1]) + ++ d(t) .$.(r(t) .|. [x(t), u1(t), u2(t)]) + +decMdp = mkTeamTime dynamics 4 + +decMdp' = simplify decMdp + diff --git a/Data/Teams/Examples/Wit79.hs b/Data/Teams/Examples/Wit79.hs new file mode 100644 --- /dev/null +++ b/Data/Teams/Examples/Wit79.hs @@ -0,0 +1,38 @@ +-- | Real time source coding +-- Based on +-- Hans S. Witsenhausen +-- "On the structure of real-time source coders," +-- Bell Systems Technical Journal, +-- vol 58, no 6, pp 1437-1451, July-August 1979 + +module Data.Teams.Examples.Wit79 where + +import Data.Teams.Structure + +x = mkNonReward "x" +x' = mkNonReward "x'" +y = mkNonReward "y" +m = mkNonReward "m" +r = mkReward "r" + +f = mkDynamics "f" +c = mkControl "c" +g = mkControl "g" +l = mkControl "l" +d = mkDynamics "d" + +dynamics t | t == 1 = f(1).$.(x(1) .|. []) + ++ c(1).$.(y(1) .|. [x(1)]) + ++ g(1).$.(x'(1).|. [y(1)]) + ++ l(1).$.(m(1) .|. [y(1)]) + ++ d(1).$.(r(1) .|. [x(1), x'(1)]) + | otherwise = f(t).$.(x(t) .|. [x(t-1)]) + ++ c(t).$.(y(t) .|. map x[1..t] ++ map y[1..t-1]) + ++ g(t).$.(x'(t).|. [y(t), m(t-1)]) + ++ l(t).$.(m(t) .|. [y(t), m(t-1)]) + ++ d(t).$.(r(t) .|. [x(t), x'(t)]) + +rt = mkTeamTime dynamics 4 + +rt' = simplify rt + diff --git a/Data/Teams/Graph.hs b/Data/Teams/Graph.hs new file mode 100644 --- /dev/null +++ b/Data/Teams/Graph.hs @@ -0,0 +1,366 @@ +-- (c) Aditya Mahajan +-- | This Haskell library implements the algorithm for simplifying sequential +-- teams presented +-- +-- Aditya Mahajan and Sekhar Tatikonda, A graphical modeling approach to +-- simplifying sequential teams, proceedings of 7th International Symposium on +-- Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks (WiOpt), +-- Control over Communication Channels (ConCom) Workshop, Seoul, South Korea, +-- June 27, 2009. +-- +-- The paper can be obtained from +-- . See +-- for a usage example. +-- +-- A team is a multi-agent stochastic control problem in which all agents have a +-- common objective. A team is sequential if and only if there is a partial +-- order between all the system variables. These partial order relationship can +-- be represented using a directed graph, in particular, using a directed factor +-- graph. The variable nodes of the factor graph represent the system variables +-- and the factor nodes represent the system dynamics and control functions. The +-- structural results for these system are equivalent to simplification of the +-- factor graph. An automated algorithm for graph simplification is presented in +-- the "Data.Teams.Structure" module. + + +module Data.Teams.Graph + ( -- * Classes + Vertex (..) + -- * Types + , Time , Variable (..) , Factor (..) , Node + , Edge , EdgeType (..) + , Team + -- * Constructors for nodes + , mkVertex , mkReward , mkNonReward , mkDynamics , mkControl + -- * Constructor for edges + , (.$.) , (.|.) + -- * Constructors for teams + , mkTeam , mkTeamTime , mkTeamTimeBy + -- * Select specific nodes + , selNodes , variables, rewards, factors, controls + -- * Graph elements + , parents , children , ancestors , ancestoral , descendants + , futureNodes , pastNodes + -- * Display functions + , printTeam , showTeam , graphToDot , printGraph + -- * Utility functions for "Data.Graph.Inductive" + , label, labels + ) where + +import qualified Data.Graph.Inductive as G +import qualified Data.GraphViz as G +import Data.Maybe (fromJust) +import Data.List (nub, intercalate, delete) +import Text.Printf (printf) + +-- | Time +type Time = Int + +-- | Variable nodes +data Variable = Reward String -- ^ Reward variable node + | NonReward String -- ^ Non reard variable node + deriving (Eq, Ord, Show) + +-- | Factor Vertexs +data Factor = Dynamics String -- ^ Factor node representing system dynamics + | Control String -- ^ Factor node representing control function + deriving (Eq, Ord, Show) + +-- | Create a sequence of nodes of a specific type +mkVertex :: (String -> a) -> String -> Time -> a +mkVertex t s = t . (s ++ ) . show + +-- | Create a sequence of reward nodes +mkReward :: String -> Time -> Variable +mkReward = mkVertex Reward + +-- | Create a sequence of non reward nodes +mkNonReward :: String -> Time -> Variable +mkNonReward = mkVertex NonReward + +-- | Create a sequence of system dynamics nodes +mkDynamics :: String -> Time -> Factor +mkDynamics = mkVertex Dynamics + +-- | Create a sequence of control nodes +mkControl :: String -> Time -> Factor +mkControl = mkVertex Control + +-- | A generic node of a graph +type Node = Either Factor Variable + +-- | A type class for defining operations on all nodes +class Vertex a where + -- | Name of node @a@ + name :: a -> String + -- | Name of a list of nodes + names :: [a] -> String + -- | Check if node @a@ is a reward node + isReward :: a -> Bool + -- | Check if node @a@ is a non reward node + isNonReward :: a -> Bool + -- | Check if node @a@ is a variable node + isVariable :: a -> Bool + -- | Check if node @a@ is a system dynamics + isDynamics :: a -> Bool + -- | Check if node @a@ is a control node + isControl :: a -> Bool + -- | Check if node @a@ is a factor node + isFactor :: a -> Bool + -- | The attributes of the node. Used to contruct the dot file. + attribute :: a -> [G.Attribute] + -- Default implmentation + names xs = "[" ++ intercalate ", " (map name xs) ++ "]" + isVariable = or . sequence [isReward, isNonReward] + isFactor = or . sequence [isControl, isDynamics] + + +instance Vertex Variable where + name (Reward a) = a + name (NonReward a) = a + + isReward (Reward _) = True + isReward (NonReward _) = False + + isNonReward (Reward _) = False + isNonReward (NonReward _) = True + + isDynamics _ = False + isControl _ = False + + attribute (Reward a) = [G.Style G.Filled, G.FillColor (G.RGB 0 255 0) + , G.Shape G.Circle + , G.Label a] + attribute (NonReward a) = [G.Shape G.Circle + , G.Label a] + +instance Vertex Factor where + name (Dynamics a) = a + name (Control a) = a + + isDynamics (Dynamics _) = True + isDynamics (Control _) = False + + isControl (Dynamics _) = False + isControl (Control _) = True + + isReward _ = False + isNonReward _ = False + + attribute (Dynamics a) = [G.Shape G.Rectangle + , G.Label a] + attribute (Control a) = [G.Style G.Filled, G.FillColor (G.RGB 255 0 0) + , G.Shape G.Rectangle + , G.Label a] + +instance (Vertex a, Vertex b) => Vertex (Either a b) where + name = either name name + isReward = either isReward isReward + isNonReward = either isNonReward isNonReward + isDynamics = either isDynamics isDynamics + isControl = either isControl isControl + attribute = either attribute attribute + +-- | An edge in a graph +type Edge = (Node, Node, EdgeType) + +-- | Currently all edges are Influence edges. Future versions will have +-- belief edges. +data EdgeType = Influence | Belief deriving (Eq, Ord, Show) + +-- | Since all edges are Influence edges, we do not differential between the +-- edges +edgeAttribute :: EdgeType -> [G.Attribute] +edgeAttribute _ = [] + +-- | Used with @(.|.)@ to specify relation between the nodes. For example, if +-- @x@ is a function of @y@ and @z@, we can write +-- +-- @f.$.(x.|.[y,z])@. + +(.$.) :: Factor -> (Variable, [Variable]) -> [Edge] +(.$.) f (x,ys) = (Left f, Right x, Influence) + : map (\y -> (Right y, Left f, Influence)) ys + +-- | Used with @(.$.)@ to specify relation between the nodes. For example, if +-- @x@ is a function of @y@ and @z@, we can write +-- +-- @f.$.(x.|.[y,z])@. +(.|.) :: Variable -> [Variable] -> (Variable, [Variable]) +(.|.) x ys = (x,ys) + +infixr 4 .|. +infixr 6 .$. + +-- | A sequential team as a directed acyclic factor graph (DAFG) +type Team = G.Gr Node EdgeType + +-- | Construct a DAFG from a set of edges. For example, +-- +-- @ +-- f = 'Control' \"f\" +-- x = 'Reward' \"x\" +-- y = 'NonReward' \"y\" +-- z = 'NonReward' \"z\" +-- g = mkTeam $ f.$.(x.|.[y,z]) +-- @ +-- +mkTeam :: [Edge] -> Team +mkTeam es = G.mkGraph nodes edges where + (nodes,nodeMap) = G.mkNodes G.new . nub . concatMap (\(a,b,_) -> [a,b]) $ es + edges = fromJust . G.mkEdges nodeMap $ es + +{- |To make a time homogeneous system. As an example, an MDP can be created as +follows + +@ +x = 'mkNonReward' \"x\" +u = 'mkNonReward' \"u\" +r = 'mkReward' \"r\" + +f = 'mkDynamics' \"f\" +g = 'mkControl' \"g\" +d = 'mkDynamics' \"d\" + +dynamics t = f(t-1).$.( x(t) .|. if t == 1 then [] else [x(t-1), u(t-1)] ) + ++ g(t) .$.( u(t) .|. map x[1..t] ++ map u[1..t-1] ) + ++ d(t) .$.( r(t) .|. [ x(t), u(t) ] ) + +mdp = 'mkTeamTime' dynamics 3 +@ +-} +mkTeamTime :: (Time -> [Edge]) -> Time -> Team +mkTeamTime dyn = mkTeamTimeBy [] dyn (const []) + +{- To make a time homogeneous system with specific start and stop dynamics +As an example, a communication system with feedback can be created as +follows. + +@ +m = 'NonReward' \"m\" +mhat = 'NonReward' \"mhat\" +r = 'Reward' \"r\" +h = 'Dynamics' \"h\" +g = 'Control' \"g\" +d = 'Dynamics' \"d\" + +x = 'mkNonReward' \"x\" +y = 'mkNonReward' \"y\" + +f = 'mkControl' \"f\" +c = 'mkDynamics' \"c\" + +start = h .$.( m .|. [] ) +dynamics t = f(t) .$. ( x(t) .|. m : map x [1..t-1] ++ map y [1..t-1] ) + ++ c(t) .$. ( y(t) .|. [ x(t) ] ) +stop t = g .$. ( mhat .|. map y [1..t] ) + ++ d .$. (r .|. [m, mhat] ) + +commfb = 'mkTeamTimeBy' start dynamics stop 3 +-} + +mkTeamTimeBy :: [Edge] -> (Time -> [Edge]) -> (Time -> [Edge]) -> Time -> Team +mkTeamTimeBy start dyn stop horizon = mkTeam nodes where + nodes = start ++ concatMap dyn [1..horizon] ++ stop horizon + + +-- * Utility functions + +-- filterNodes :: (Node -> Bool) -> Team -> [G.Node] -> [G.Node] +-- filterNodes p team = filter (p . label team) + +-- | Select nodes whose label satisfy a particular predicate +selNodes :: G.Graph gr => (a -> Bool) -> gr a b -> [G.Node] +selNodes p = map G.node' . G.gsel (p.G.lab') + +-- | All variable nods +variables :: Team -> [G.Node] +variables = selNodes isVariable + +-- | All reward nodes +rewards :: Team -> [G.Node] +rewards = selNodes isReward + +-- | All control factors +controls :: Team -> [G.Node] +controls = selNodes isControl + +-- | All factors +factors :: Team -> [G.Node] +factors = selNodes isFactor + +-- * Graph relations + +-- | find indices of parents from the index of a node +parents :: Team -> G.Node -> [G.Node] +parents = G.pre + +-- | find indices of children from the index of a node +children :: Team -> G.Node -> [G.Node] +children = G.suc + +-- | find indices of descendants from the index of a node +descendants :: Team -> G.Node -> [G.Node] +descendants team idx = idx `delete` G.reachable idx team + +-- | find indices of ancestors from the index of a node +ancestors :: Team -> G.Node -> [G.Node] +ancestors team idx = idx `delete` G.reachable idx (G.grev team) + +-- | find the indices of the ancestoral set from the indices of a given set. +ancestoral :: Team -> [G.Node] -> [G.Node] +ancestoral team = nub . concatMap (flip G.reachable (G.grev team)) + +-- | find the indices of future nodes that satisfy a particular predicate +futureNodes :: Team -> (Node -> Bool) -> G.Node -> [G.Node] +futureNodes team p = filter (p . label team) . descendants team + +-- | find the indices of past nodes that satisfy a particular predicate +pastNodes :: Team -> (Node -> Bool) -> G.Node -> [G.Node] +pastNodes team p = filter (p . label team) . ancestors team + + +-- * Display functions + +-- | Pretty print the team specification +printTeam :: Team -> IO () +printTeam = putStr . showTeam + +-- | Pretty print the team specification +showTeam :: Team -> String +showTeam team = showTeamBy team isDynamics "Dynamics:" ++ "\n" + ++ showTeamBy team isControl "Control :" ++ "\n" + +showTeamBy :: Team -> (Node -> Bool) -> String -> String +showTeamBy team p str = if null equations + then "" + else unlines (header ++ equations) + where header = [str, map (const '=') str] + equations = map showFactor . filter (p.snd) . G.labNodes $ team + showFactor (idx,lab) = printf "%s.$.(%s.|.%s)" (name lab) + (names.labels team $ suc) + (names.labels team $ pre) + where suc = G.suc team idx + pre = G.pre team idx + + +-- * Convert to Graphviz graphs + +-- | Convert the graph to a dot file +graphToDot :: Team -> G.DotGraph +graphToDot team = G.graphToDot team [] (attribute.snd) + (edgeAttribute. \(_,_,b) -> b) + +-- | Convert the dot file to a pdf +printGraph :: Team -> FilePath -> IO Bool +printGraph team = G.runGraphviz (graphToDot team) G.Pdf + +-- | Extensions of Data.Graph.Inductive + +-- | Label of a particular node +label :: G.Graph gr => gr a b -> G.Node -> a +label gr = fromJust . G.lab gr + +-- | Labels of a list of nodes +labels :: G.Graph gr => gr a b -> [G.Node] -> [a] +labels = map . label diff --git a/Data/Teams/Structure.hs b/Data/Teams/Structure.hs new file mode 100644 --- /dev/null +++ b/Data/Teams/Structure.hs @@ -0,0 +1,324 @@ +-- (c) Aditya Mahajan +{- | + +This module implments an automated algortihm to simplify sequential teams. The +simplification is based on conditional independences. Conditional independence +is checked using the Bayes Ball algorithm + + +-} + +module Data.Teams.Structure + ( module Data.Teams.Graph + -- * Determine conditional independence + , observations , irrelevant , determined , effective + -- * Structural results for teams + , simplifyAt , simplifyOnce , simplify + ) where + +import Data.Teams.Graph +import qualified Data.Graph.Inductive as G +import Data.List (intersect, (\\) ) +import Debug.Trace + + +{- +The Bayes Ball algortihm keeps track of a state for each node. The state +consists of a mark (indicating if it has been visited from top or bottom +before), a schedule (indicating if it was scheduled to be visited from top or +bottom), and a flag (indicating if it has been visited or not). +-} + +-- | Mark +data Mark = NotMarked | TopMarked | BottomMarked | BothMarked + deriving (Eq, Ord, Show) + +-- | Change mark +chMark :: Mark -> Mark -> Mark +chMark NotMarked a = a +chMark _ NotMarked = NotMarked +chMark BothMarked _ = BothMarked +chMark _ BothMarked = BothMarked +chMark BottomMarked TopMarked = BothMarked +chMark TopMarked BottomMarked = BothMarked +chMark BottomMarked BottomMarked = BottomMarked +chMark TopMarked TopMarked = TopMarked + +-- | Schedule +data Schedule = NotScheduled | TopScheduled | BottomScheduled | BothScheduled + deriving (Eq, Ord, Show) + +-- | Change schedule +chSchedule :: Schedule -> Schedule -> Schedule +chSchedule NotScheduled a = a +chSchedule _ NotScheduled = NotScheduled +chSchedule BothScheduled _ = BothScheduled +chSchedule _ BothScheduled = BothScheduled +chSchedule BottomScheduled TopScheduled = BothScheduled +chSchedule TopScheduled BottomScheduled = BothScheduled +chSchedule BottomScheduled BottomScheduled = BottomScheduled +chSchedule TopScheduled TopScheduled = TopScheduled + +-- | Visit +data Visit = Visited | NotVisited + deriving (Eq, Ord, Show) + +-- | A marked node of a graph +data Marked = VMarked Variable Mark Schedule Visit + | FMarked Factor Mark Schedule Visit + deriving (Eq, Ord, Show) + +-- | The mark of a marked node +mark :: Marked -> Mark +mark (VMarked _ m _ _) = m +mark (FMarked _ m _ _) = m + +-- | The node label of the marked node +node :: Marked -> Node +node (VMarked a _ _ _) = Right a +node (FMarked a _ _ _) = Left a + +-- | The scedule of a marked node +schedule :: Marked -> Schedule +schedule (VMarked _ _ s _) = s +schedule (FMarked _ _ s _) = s + +-- | The visit status of a marked node +visit :: Marked -> Visit +visit (VMarked _ _ _ v) = v +visit (FMarked _ _ _ v) = v + +-- | Add a mark to a marked node +addMark :: Mark -> Marked -> Marked +addMark n (VMarked a m s v) = VMarked a (chMark m n) s v +addMark n (FMarked a m s v) = FMarked a (chMark m n) s v + +-- | Add a schedule to a marked node +addSchedule :: Schedule -> Marked -> Marked +addSchedule n (VMarked a m s v) = VMarked a m (chSchedule s n) v +addSchedule n (FMarked a m s v) = FMarked a m (chSchedule s n) v + +-- | Add a visit to a marked node +addVisit :: Marked -> Marked +addVisit (VMarked a m s _) = VMarked a m s Visited +addVisit (FMarked a m s _) = FMarked a m s Visited + +-- | Remove all flags from the marked node +clean :: Marked -> Marked +clean (VMarked a _ _ _) = VMarked a NotMarked NotScheduled NotVisited +clean (FMarked a _ _ _) = FMarked a NotMarked NotScheduled NotVisited + +-- | Check if a marked node is marked on top +isTopMarked :: Marked -> Bool +isTopMarked n = let m = mark n in (m==TopMarked || m == BothMarked) + +-- | Check if a marked node is marked on bottom +isBottomMarked :: Marked -> Bool +isBottomMarked n = let m = mark n in (m==BottomMarked || m == BothMarked) + +-- | Check if a marked node is scheduled +isScheduled :: Marked -> Bool +isScheduled n = NotScheduled /= schedule n + +-- | Check if a marked node is visited +isVisited :: Marked -> Bool +isVisited n = Visited == visit n + +-- | A class to convert a normal graph to a marked graph +class Initializable a where + mkClean :: a -> Marked + +instance Initializable Variable where + mkClean v@(Reward _) = VMarked v NotMarked NotScheduled NotVisited + mkClean v@(NonReward _) = VMarked v NotMarked NotScheduled NotVisited + +instance Initializable Factor where + mkClean f@(Dynamics _) = FMarked f NotMarked NotScheduled NotVisited + mkClean f@(Control _) = FMarked f NotMarked NotScheduled NotVisited + +instance (Initializable a, Initializable b) => Initializable (Either a b) where + mkClean (Left a) = mkClean a + mkClean (Right a) = mkClean a + +-- | A marked gream +type MTeam = G.Gr Marked EdgeType + +-- | All scheduled nodes +scheduledNodes :: MTeam -> [G.Node] +scheduledNodes = selNodes isScheduled + +-- | The Bayes Ball algorithm +bayesBall :: Team -> [G.Node] -> [G.Node] -> MTeam +bayesBall team condition reward = doBayesBall condition mteam where + -- Initialize all nodes as neither marked, nor scheduled, nor visited + -- Then schedule all reward nodes to be visited from bottom. + mteam = G.gmap initialize . G.nmap mkClean $ team + initialize (pre,idx,lab,suc) = (pre, idx, lab', suc) + where lab' = if idx `elem` reward + then addSchedule BottomScheduled lab + else lab + +-- | The main loop of the Bayes Ball algorithm +doBayesBall :: [G.Node] -> MTeam -> MTeam +doBayesBall condition gr = case scheduledNodes gr of + -- If there are no more scheduled nodes, then we are done. + [] -> gr + -- Otherwise we modify the graph and loop again + (x:_) -> doBayesBall condition (modify gr) where + modify | isFactor . node $ mLabel = modifyFactor + | otherwise = modifyVariable + where mLabel = label gr x + mSchedule = schedule mLabel + + -- If we are a factor node, let the ball pass through + -- Do not mark the node + modifyFactor = case mSchedule of + BottomScheduled -> markClean . bottomThrough + TopScheduled -> markClean . topThrough + BothScheduled -> markClean . bothThrough + NotScheduled -> error ("Node " ++ show x ++ " not scheduled") + + -- If we are at a variable node, bounce the ball intelligently + -- Then mark the nodes as visited and not scheduled. + modifyVariable = case mSchedule of + BottomScheduled -> markVisited . bottomVisit + TopScheduled -> markVisited . topVisit + BothScheduled -> markVisited . bothVisit + NotScheduled -> error ("Node " ++ show x ++ " not scheduled") + + -- When the visit is from bottom, if the node is in the + -- conditioning nodes, do nothing. Otherwise, if the bottom of the + -- node is not marked, mark the bottom and schedule all of its + -- parents (pass the ball). Further, if the node is not a + -- deterministic node, mark its top and visit all its children + -- (bounce the ball) + bottomVisit | x `elem` condition = id + | otherwise = checkAction . markBottom + -- Check if a node is a deterministic node or not. + checkAction | isDeterministic gr x = id + | otherwise = markTop + -- When the visit is from the top, is the node is in the + -- conditioning node and its bottom is not marked, mark its bottom + -- and schedule all of its parents to be visisted (bounce the + -- ball). Otherwise, if the node is not in the conditioning nodes + -- and its top is not marked, mark its top and schedule all of its + -- children (pass the ball) + topVisit | x `elem` condition = markBottom + | otherwise = markTop + -- When the visit is both from the top and bottom, combine the + -- actions. + bothVisit | x `elem` condition = markBottom + | otherwise = markTop . markBottom + + -- To mark the top. If the top is not marked, mark the top and pass + -- the ball throgh. Otherwise, swallow the ball. + markTop g | not . isTopMarked . label g $ x = + topThrough (markNode TopMarked x g) + | otherwise = g + + -- To mark the bottom. If the bottom is not marked, mark the bottom + -- and pass the ball throgh. Otherwise, swallow the ball. + markBottom g | not . isBottomMarked . label g $ x = + bottomThrough (markNode BottomMarked x g) + | otherwise = g + + -- Passing the ball through + topThrough g = scheduleNodes TopScheduled g (G.suc g x) + bottomThrough g = scheduleNodes BottomScheduled g (G.pre g x) + bothThrough = topThrough . bottomThrough + + -- Marking the node visited or clean + markVisited{- g -} = visitNode x -- g + markClean {- g -} = cleanNode x -- g + +-- | Check if a node is deterministic. Currently we simply check if its parent +-- is a control node. +isDeterministic :: MTeam -> G.Node -> Bool +isDeterministic mteam x = case G.pre mteam x of + [] -> True + [y] -> isControl. node . label mteam $ y + _ -> False + +-- | Modify a marked node +modifyNode :: (a -> Marked -> Marked) -> a -> G.Node -> MTeam -> MTeam +modifyNode f m x mteam = case G.match x mteam of + (Nothing, _ ) -> error ("Cannot modify node " ++ show x ++ " : Not in graph") + (Just (pre,idx,lab,suc), gr') -> (pre, idx, f m lab, suc) G.& gr' + +-- | Mark a node +markNode :: Mark -> G.Node -> MTeam -> MTeam +markNode = modifyNode addMark + +-- | Schedule a node +scheduleNode :: Schedule -> G.Node -> MTeam -> MTeam +scheduleNode = modifyNode addSchedule + +-- | Schedule a list of nodes +scheduleNodes :: Schedule -> MTeam -> [G.Node] -> MTeam +scheduleNodes = foldr . scheduleNode + +-- | Visit a node +visitNode :: G.Node -> MTeam -> MTeam +visitNode = modifyNode (\s -> addSchedule s . addVisit) NotScheduled + +-- | Clean a node of all marked +cleanNode :: G.Node -> MTeam -> MTeam +cleanNode = modifyNode (const clean) id + +-- | Filter out the result from the bayes ball algortihm +result :: (Marked -> Bool) -> Team -> [G.Node] -> [G.Node] -> [G.Node] +result p team condition = map fst . filter (p.snd) . G.labNodes + . bayesBall team condition + +-- | Irrelevant nodes +-- The nodes that have not been visited from their parents are irrelevant +irrelevant :: Team -> [G.Node] -> [G.Node] -> [G.Node] +irrelevant = result (and . sequence [not.isTopMarked, isVariable.node] ) + +-- | Requisite observations +-- The observation nodes are thouse nodes in the condition that are marked as +-- visited +observations :: Team -> [G.Node] -> [G.Node] -> [G.Node] +observations team condition reward = condition `intersect` + result isVisited team condition reward + +-- | Functionally determined nodes +-- Nodes that are irrelevant when we want to know about all variable nodes +determined :: Team -> [G.Node] -> [G.Node] +determined team var = irrelevant team var (variables team) + +-- | Effectively observed nodes +-- All the ancestors of the reward nodes that are functionally determined by +-- conditioned nodes. +effective :: Team -> [G.Node] -> [G.Node] -> [G.Node] +effective team conditioned reward = (determined team conditioned `intersect` + ancestoral team reward) \\ conditioned + +-- | The graph restructuring algorithm of the paper. +simplifyAt :: Team -> G.Node -> Team +simplifyAt team control = G.insEdges insEdges . G.delEdges delEdges $ team where + pa = parents team control + ch = children team control + ne = ch ++ pa + de = descendants team control + rd = futureNodes team isReward control + ob = observations team ne rd \\ ch + ef = effective team pa rd \\ de + delEdges = map (\ a -> (a, control)) (pa \\ ob) + insEdges = map (\ a -> (a, control, Influence)) (ef \\ de) + +-- | Simplify all nodes of the graph once +simplifyOnce :: Team -> Team +simplifyOnce team = foldr (flip simplifyAt) team (controls team) where + +-- | The graph simplification aglorithm of the paper +-- I believe that this algorithm will always converge. So, I do not stop the +-- loop after a finite number of iterations. If you find an example that does +-- not converge, please let me know. +simplify :: Team -> Team +simplify team = untilEqual . zip stream $ [(1::Int)..] where + stream = iterate simplifyOnce team + untilEqual ((a,n):as@((b,_):_)) = trace ("Simplify : Iteration " ++ show n) $ + if G.equal a b then a + else untilEqual as + untilEqual _ = error "Infinite stream ended. This should not happen" diff --git a/LICENSE b/LICENSE new file mode 100644 --- /dev/null +++ b/LICENSE @@ -0,0 +1,674 @@ + GNU GENERAL PUBLIC LICENSE + Version 3, 29 June 2007 + + Copyright (C) 2007 Free Software Foundation, Inc. + Everyone is permitted to copy and distribute verbatim copies + of this license document, but changing it is not allowed. + + Preamble + + The GNU General Public License is a free, copyleft license for +software and other kinds of works. + + The licenses for most software and other practical works are designed +to take away your freedom to share and change the works. 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But first, please read +. diff --git a/Setup.hs b/Setup.hs new file mode 100644 --- /dev/null +++ b/Setup.hs @@ -0,0 +1,2 @@ +import Distribution.Simple +main = defaultMain diff --git a/teams.cabal b/teams.cabal new file mode 100644 --- /dev/null +++ b/teams.cabal @@ -0,0 +1,19 @@ +Name: teams +Version: 0.0.1 +Description: Graphical modeling tools for sequential teams +License: GPL +License-file: LICENSE +Author: Aditya Mahajan +Maintainer: aditya DOT mahajan AT yale DOT edu +Build-Type: Simple +Cabal-Version: >=1.2 +Category: Algorithms, Stochastic Control +Stability: experimental +Synopsis: Graphical modeling tools for sequential teams +Library + Build-Depends: base, fgl>=5.4, containers, graphviz>=2009.5.1 + Exposed-modules: Data.Teams.Graph + Data.Teams.Structure + Data.Teams.Examples.Wit79 + Data.Teams.Examples.DecMdp + ghc-options: -Wall