Screen rights to Algren's novel were first acquired in 1949 on behalf of John Garfield, who planned to star in the film version. However, production was delayed because the Production Code Authority (PCA) refused to approve the script, with Joseph Breen stating that the basic story was "unacceptable" because of the Code's prohibition on showing illegal drug trafficking and drug addiction. The ability to obtain PCA approval was critical because at that time, many movie theaters would not show films that had not received approval. The PCA further predicted that the subject would also be unacceptable to the National Legion of Decency (a Catholic film censor board), Federal authorities, and state and local censor boards in the United States and abroad. Garfield died in 1952 and director Otto Preminger acquired the rights from his estate.  Preminger had previously released The Moon Is Blue (1953), which succeeded at the box office despite being denied the Production Code seal of approval due to its sexual subject matter. He told Peter Bogdanovich why he was attracted to Algren's novel: "I think there's a great tragedy in any human being who gets hooked on something, whether it's heroin or love or a woman or whatever." Although United Artists (UA) had a distribution contract with Preminger, a clause in the contract allowed them to withdraw if a film failed to get Code approval. Preminger stated that in that event, he would set up his own company to handle distribution of The Man With The Golden Arm. Preminger continued to have problems with the PCA during the making of the film.  Although the novel's author, Nelson Algren, was initially brought to Hollywood to work on the screenplay, he and Preminger did not get along, and he was quickly replaced by Walter Newman. Preminger and Newman went on to make significant changes to Algren's original story, and the film was eventually released as "A Film By Otto Preminger". In 1956, Algren sued Preminger and others seeking an injunction to keep Preminger from claiming authorship of the film, but had to drop the suit because he could not afford the legal fees.  Frank Sinatra jumped at a chance to star in the film before reading the entire script. The script was given to Marlon Brando around the same time as Sinatra, who still harbored some anger at Brando for beating out Sinatra for the lead role in On the Waterfront. To prepare for his role, Sinatra spent time at drug rehabilitation clinics observing addicts going cold turkey. He also learned to play drums from drummer Shelly Manne. The picture was shot in six weeks at RKO Studios in Hollywood from September 26 through November 4, 1955.  Saul Bass designed the crooked arm symbol used in the film's advertising campaign, which Preminger liked so much that he threatened to pull the picture if an exhibitor changed the advertisements. Bass also created the animated title sequence for the film, the first of many such sequences that he created for films by Preminger, Alfred Hitchcock, and others.

Answer this question "When did production begin for the film?" by extracting the answer from the text above.
The picture was shot in six weeks at RKO Studios in Hollywood from September 26 through November 4, 1955.